Mr. Flynn, who served in the job for less than a month, said he had given “incomplete information” regarding a telephone call he had with the ambassador in late December about American sanctions against Russia, weeks before President Trump’s inauguration. Mr. Flynn previously had denied that he had any substantive conversations with Ambassador Sergey I. Kislyak, and Mr. Pence repeated that claim in television interviews as recently as this month.

But on Monday, a former administration official said the Justice Department warned the White House last month that Mr. Flynn had not been fully forthright about his conversations with the ambassador. As a result, the Justice Department feared that Mr. Flynn could be vulnerable to blackmail by Moscow.

In his resignation letter, which the White House emailed to reporters, Mr. Flynn said he had held numerous calls with foreign officials during the transition. “Unfortunately, because of the fast pace of events, I inadvertently briefed the vice president-elect and others with incomplete information regarding my phone calls with the Russian ambassador,” he wrote. “I have sincerely apologized to the president and the vice president, and they have accepted my apology.”

“I am tendering my resignation, honored to have served our nation and the American people in such a distinguished way,” Mr. Flynn wrote.

The White House said in the statement that it was replacing Mr. Flynn with retired Lt. Gen. Joseph K. Kellogg Jr. of the Army, a Vietnam War veteran, as acting national security adviser.

Mr. Flynn was an early and ardent supporter of Mr. Trump’s candidacy, and in his resignation he sought to praise the president. “In just three weeks,” Mr. Flynn said, the new president “has reoriented American foreign policy in fundamental ways to restore America’s leadership position in the world.”

But in doing so, he inadvertently illustrated the brevity of his tumultuous run at the National Security Council, and the chaos that has gripped the White House in the first weeks of the Trump administration — and created a sense of uncertainty around the world.

Earlier Monday, Sean Spicer, the White House press secretary, told reporters that “the president is evaluating the situation” about Mr. Flynn’s future. By Monday evening, Mr. Flynn’s fortunes were rapidly shifting — his resignation came roughly seven hours after Kellyanne Conway, a counselor to the president, said on MSNBC that Mr. Trump had “full confidence” in the retired general.

And when he did step down, it happened so quickly that his resignation does not appear to have been communicated to National Security Council staff members, two of whom said they learned about it from news reports.

Officials said Mr. Pence had told others in the White House that he believed Mr. Flynn lied to him by saying he had not discussed the topic of sanctions on a call with the Russian ambassador in late December. Even the mere discussion of policy — and the apparent attempt to assuage the concerns of an American adversary before Mr. Trump took office — represented a remarkable breach of protocol.

The F.B.I. had been examining Mr. Flynn’s phone calls as he came under growing questions about his interactions with Russian officials and his management of the National Security Council. The blackmail risk envisioned by the Justice Department would have stemmed directly from Mr. Flynn’s attempt to cover his tracks with his bosses. The Russians knew what had been said on the call; thus, if they wanted Mr. Flynn to do something, they could have threatened to expose the lie if he refused.

The Justice Department’s warning to the White House was first reported on Monday night by The Washington Post.

In addition, the Army has been investigating whether Mr. Flynn received money from the Russian government during a trip he took to Moscow in 2015, according to two defense officials. Such a payment might violate the Emoluments Clause of the Constitution, which prohibits former military officers from receiving money from a foreign government without consent from Congress. The defense officials said there was no record that Mr. Flynn, a retired three-star Army general, filed the required paperwork for the trip.

Representative Adam B. Schiff of California, the top Democrat on the House Intelligence Committee, said in a statement late Monday that Mr. Flynn’s resignation would not close the question of his contact with Russian officials.

“General Flynn’s decision to step down as national security adviser was all but ordained the day he misled the country about his secret talks with the Russian ambassador,” said Mr. Schiff, noting that the matter is still under investigation by the House committee.

Two other Democratic lawmakers — Representative John Conyers Jr. of Michigan and Representative Elijah E. Cummings of Maryland — called for an immediate briefing by the Justice Department and the F.B.I. over the “alarming new disclosures” that Mr. Flynn was a blackmail risk. “We need to know who else within the White House is a current and ongoing risk to our national security,” they said in a statement.

Representative Devin Nunes, Republican of California and the chairman of the House intelligence committee, was supportive of Mr. Flynn until the end. “Washington, D.C., can be a rough town for honorable people, and Flynn — who has always been a soldier, not a politician — deserves America’s gratitude and respect,” Mr. Nunes said in a statement.

The White House had examined a transcript of a wiretapped conversation that Mr. Flynn had with Mr. Kislyak in December, according to administration officials. Mr. Flynn originally told Mr. Pence and others that the call was limited to small talk and holiday pleasantries.

But the conversation, according to officials who saw the transcript of the wiretap, also included a discussion about sanctions imposed on Russia after intelligence agencies determined that President Vladimir V. Putin’s government tried to interfere with the 2016 election on Mr. Trump’s behalf. Still, current and former administration officials familiar with the call said the transcript was ambiguous enough that Mr. Trump could have justified either firing or retaining Mr. Flynn.

Mr. Trump, however, had become increasingly concerned about the continued fallout over Mr. Flynn’s behavior, according to people familiar with his thinking, and told aides that the media storm around Mr. Flynn would damage the president’s image on national security issues.

Stephen K. Bannon, the president’s chief strategist, asked for Mr. Flynn’s resignation — a move that he has been pushing for since Friday, when it became clear that the national security adviser had misled Mr. Pence.

Around 8:20 p.m. Monday, a sullen Mr. Flynn was seen in the Oval Office, just as preparations were being made for the swearing-in of newly confirmed Treasury Secretary Steven T. Mnuchin. Soon after, Mr. Flynn’s resignation letter started making the rounds.

Administration officials said it was unlikely that Mr. Kellogg would be asked to stay on as Mr. Flynn’s permanent replacement. Mr. Flynn brought Mr. Kellogg into the Trump campaign, according to a former campaign adviser, and the two have remained close. K. T. McFarland, the deputy national security adviser who also was brought on by Mr. Flynn, is expected to leave that role, a senior official said.

One person close to the administration, who was not authorized to discuss the personnel moves and spoke on the condition of anonymity, said that retired Vice Admiral Robert S. Harward is the leading candidate to replace Mr. Flynn, although Mr. Kellogg and David H. Petraeus are being discussed. It was not clear whether Mr. Petraeus is still expected to appear at the White House this week, as initially discussed by advisers to the president.

Mr. Flynn’s concealment of the call’s content, combined with questions about his management of his agency and reports of a demoralized staff, put him in a precarious position less than a month into Mr. Trump’s presidency.

Few members of Mr. Trump’s team were more skeptical of Mr. Flynn than the vice president, numerous administration officials said. Mr. Pence, who used the false information provided by Mr. Flynn to defend him in a series of television appearances, was incensed at Mr. Flynn’s lack of contrition for repeatedly embarrassing him by withholding the information, according to three administration officials familiar with the situation.

Mr. Flynn and Mr. Pence spoke twice in the past few days about the matter, but administration officials said that rather than fully apologize and accept responsibility, the national security adviser blamed his faulty memory — which irked the typically slow-to-anger Mr. Pence.

The slight was compounded by an episode late last year when Mr. Pence went on television to deny that Mr. Flynn’s son, who had posted conspiracy theories about Hillary Clinton on social media, had been given a security clearance by the transition team. The younger Mr. Flynn had, indeed, been given such a clearance, even though his father had told Mr. Pence’s team that he had not.

Officials said classified information did not appear to have been discussed during the conversation between Mr. Flynn and the ambassador, which would have been a crime. The call was captured on a routine wiretap of diplomats’ calls, the officials said.

But current Trump administration officials and former Obama administration officials said that Mr. Flynn did appear to be reassuring the ambassador that Mr. Trump would adopt a more accommodating tone on Russia once in office.

Former and current administration officials said that Mr. Flynn urged Russia not to retaliate against any sanctions because an overreaction would make any future cooperation more complicated. He never explicitly promised sanctions relief, one former official said, but he appeared to leave the impression that it would be possible.

During his 2015 trip to Moscow, Mr. Flynn was paid to attend the anniversary celebration of Russia Today, a television network controlled by the Kremlin. At the banquet, he sat next to Mr. Putin.

Mr. Flynn had notified the Defense Intelligence Agency, which he once led, that he was taking the trip. He received a security briefing from agency officials before he left, which is customary for former top agency officials when they travel overseas.

Still, some senior agency officials were surprised when footage of the banquet appeared on RT, and believed that Mr. Flynn should have been more forthcoming with the agency about the nature of his trip to Russia.

Correction: February 13, 2017

An earlier version of this article misstated the day on which the White House sent out a series of conflicting signals about Michael T. Flynn, the national security adviser. It was Monday, not Tuesday. Also, because of an editing error, an earlier version quoted three posts from an unverified Twitter account purporting to be Mr. Flynn’s, responding to the resignation.

(http://www.autoadmit.com/thread.php?thread_id=3525723&forum_id=2#32619006)