WASHINGTON — Michael T. Flynn, President Trump’s former national security adviser, misled Pentagon investigators about his income from companies in Russia and contacts with officials there when he applied for a renewal of his top-secret security clearance last year, according to a letter released Monday by the top Democrat on the House oversight committee.

Mr. Flynn, who resigned 24 days into the Trump administration, told investigators in February 2016 that he had received no income from foreign companies and had only “insubstantial contact” with foreign nationals, according to the letter. In fact, Mr. Flynn had sat two months earlier beside President Vladimir V. Putin of Russia at a Moscow gala for RT, the Kremlin-financed television network, which paid him more than $45,000 to attend the event and give a separate speech.

His failure to make those disclosures and his apparent attempt to mislead the Pentagon could put Mr. Flynn in further legal jeopardy. Intentionally lying to federal investigators is a felony punishable by up to five years in prison. Separately, he also faces legal questions over failing to properly register as a foreign agent for lobbying he did last year on behalf of Turkey while advising the Trump campaign, which is also a felony.

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The House letter, written by Representative Elijah E. Cummings of Maryland, was made public hours after Mr. Flynn formally rejected a subpoena from senators investigating Russian interference in the 2016 election and chose to instead invoke his right against self-incrimination, a person familiar with his decision said.

Mr. Flynn had been ordered by the Senate Intelligence Committee to hand over emails and other records related to any dealings with Russians as part of that panel’s investigation into Russian meddling in the 2016 election. His decision to invoke his Fifth Amendment right puts him at risk of being held in contempt of Congress, which can also result in a criminal charge.

In a letter to the heads of the Intelligence Committee, Mr. Flynn’s lawyers said that the accusations against him, as well as the appointment of a special counsel to oversee the Justice Department investigation into Russian election interference, gave him “reasonable cause to apprehend danger” should he comply with the subpoena.

“He is the target on a nearly daily basis of outrageous allegations, often attributed to anonymous sources in Congress or elsewhere in the United States government, which, however fanciful on their face and unsubstantiated by evidence, feed the escalating public frenzy against him,” his lawyers wrote.

They also reiterated his willingness to testify in exchange for immunity. A lawyer for Mr. Flynn, Robert Kelner, did not respond to a request for comment about Mr. Cummings’s letter.

The controversies surrounding the Trump White House’s ties to Russia have overshadowed the early months of the new administration, and Mr. Flynn has been at the center of the maelstrom. He is under scrutiny both by congressional committees and by federal law enforcement agencies for his ties to Russia and his business dealings with Turkey.

Document | Cummings Urges Chaffetz to Subpoena Flynn In a letter to Representative Jason Chaffetz, the chairman of the House Oversight Committee, Representative Elijah E. Cummings, the ranking minority member, requested a subpoena for documents related to any connections between Michael T. Flynn, the former national security adviser, and Russia. In the request, Mr. Cummings highlights an encounter between Mr. Flynn and high-level Russian officials that he failed to disclose for a security clearance check as reasoning for the subpoena.

In February, Mr. Trump asked James B. Comey, then the F.B.I. director, to end the bureau’s investigation into Mr. Flynn, a request some legal experts have said amounts to obstruction of justice.

Lawmakers previously said that Mr. Flynn had failed to disclose the income he received for the Moscow trip when he was seeking clearance to work in the White House. The letter released Monday showed that he had misled investigators during a previous attempt to renew his clearance, months before Mr. Trump was elected.

Mr. Cummings’s letter indicated that Mr. Flynn misled Pentagon investigators during the clearance process, including during an in-person interview in February 2016. Mr. Cummings quoted directly from the Pentagon report detailing Mr. Flynn’s clearance process. The document itself was not included with his letter, sent to Representative Jason Chaffetz, the Utah Republican who is the chairman of the oversight committee.

As Mr. Flynn’s legal problems have accumulated, White House officials have tried to distance themselves from him. They have also tried to shift blame, pointing out that it was during the Obama administration that his security clearance was renewed. Mr. Flynn, a former three-star general, ran the Defense Intelligence Agency from mid-2012 until 2014.

The House committee has asked the White House to turn over all documents used by Mr. Trump’s transition team to vet Mr. Flynn, as well as any communications among Mr. Trump’s top aides about Mr. Flynn’s contacts with foreign officials.

The White House has thus far refused to comply with the request. Mr. Cummings has been pushing Mr. Chaffetz to issue a subpoena demanding the documents.

“In refusing our requests for a subpoena, you have made the same argument as President Trump — that you believe the White House bears no responsibility for vetting General Flynn for the position of national security adviser because he received his latest security clearance renewal under the Obama administration in early 2016,” Mr. Cummings wrote to Mr. Chaffetz.

Previous documents released by the oversight committee revealed that Mr. Flynn was paid more than $65,000 by companies linked to Russia in 2015. In addition to RT, he received $11,250 from a Russian cargo airline, Volga-Dnepr Airlines, which had been implicated in a bribery scheme involving Russian officials at the United Nations. In October 2015, he was paid another $11,250 by Kaspersky Government Security Solutions, the American branch of a Russian cybersecurity firm.

Retired generals are ordinarily allowed to keep a clearance as a courtesy, but they must report all income from foreign sources to the Pentagon. Possessing a security clearance opens up potentially lucrative jobs with government contractors, who prize contacts and insider knowledge.

In a letter to Congress last month, the Pentagon’s acting inspector general, Glenn A. Fine, said his office had opened an investigation into whether Mr. Flynn failed to properly report income from foreign governments.

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As for his refusal to comply with the Senate’s subpoena, it is up to lawmakers to decide whether to hold him in contempt of Congress. Mr. Flynn said in March that he would talk to congressional investigators in exchange for immunity from prosecution. Lawmakers declined his offer, though they did not rule out the possibility of revisiting the issue.

Senators Richard M. Burr of North Carolina and Mark Warner of Virginia, the committee’s Republican chairman and Democratic vice chairman, vowed in a statement to continue seeking the documents, as well as Mr. Flynn’s testimony.

Two other people in Mr. Trump’s orbit during the campaign — Roger Stone, a longtime adviser, and Paul Manafort, his former campaign chairman — have provided some documents requested by the Senate Intelligence Committee, a person close to the investigation said Monday.

Mr. Flynn’s decision was first reported by The Associated Press.

His assertion of the Fifth Amendment may not hold up in court. Raymond Granger, a New York-based lawyer and former state and federal prosecutor, said it was “a common mistake” for witnesses to try to apply their right to protect themselves against self-incrimination to documents.

“However, if they try to litigate this, they would lose quickly and badly,” Mr. Granger said of Mr. Flynn’s lawyers. He said the Fifth Amendment generally does not apply to documents because it is intended to shield Americans from having their compelled statements used against them — not statements made voluntarily, such as on a document, or supplied by a third party.

Mr. Flynn’s lawyers disputed that notion in their letter, referring to producing the documents as “a testimonial act” that would be protected by the Fifth Amendment.

Should he testify before the committee, Mr. Flynn could invoke his Fifth Amendment right at that time.

Gov. Chris Christie of New Jersey, who ran Mr. Trump’s transition team until a few days after the election, said publicly for the first time Monday that he had advised Mr. Trump against selecting Mr. Flynn for a White House position.

“It’s safe to say that General Flynn and I didn’t see eye to eye,” Mr. Christie told reporters during a news conference in Trenton. “And that I didn’t think that he was someone who would bring benefit to the president or to the administration. And I made that very clear to candidate Trump, and I made it very clear to President-elect Trump.”

Separately, Mr. Chaffetz said he had decided to postpone a potential oversight committee hearing with testimony from Mr. Comey after the two spoke Monday.

“He wants to speak with special counsel prior to public testimony,” Mr. Chaffetz said on Twitter, referring to Robert S. Mueller III, who was appointed last week to lead the federal investigation into Russian election meddling.