Chaffetz and Cummings stressed that as a former military officer, Flynn would have needed special permission for his appearance at a gala sponsored by RT, the Russian-Government-funded television station, for which he was paid US$45,000. For his work lobbying on behalf of the Turkish Government, he was paid more than US$500,000.
"It does not appear that was ever sought, nor did he get that permission," Chaffetz said.
The Republican later added that while Flynn was clearly not in compliance with the law, "it would be a little strong to say that he flat-out lied".
Flynn's omission could cost him. Violations of this nature can be punished by up to five years of jail time, though President Donald Trump's Justice Department ultimately would make the decision about whether to investigate or charge him.
Chaffetz stressed that the Government ought to "recover the money" that was paid to Flynn by foreign entities - a figure that would at least be in the tens of thousands of dollars.
While it will not be up to the Oversight Committee to impose punishment, panel leaders pledged to pursue the matter, indicating a preference for making the documents the lawmakers reviewed public.
The future of any action may rely on a new Oversight Committee chairman. Chaffetz announced last week that he would resign from Congress in 2018 and perhaps leave much sooner - setting off a scramble to replace him on the House's chief investigative panel.
The documents that committee members reviewed came from the Defence Intelligence Agency and showed that Flynn had not declared any income from Russian or Turkish sources, despite the fact that the forms were filed about a month after Flynn's reported trip to Moscow to speak at the RT gala, Cummings said.
Flynn, a Trump campaign adviser and the first national security adviser of the Trump Administration, was ousted in February after it was revealed that he misled Vice-President Pence about his talks at the end of 2016 with the Russian ambassador to the United States.
The FBI and the House and Senate intelligence committees are investigating Russia's alleged meddling in the 2016 election, supposedly to help Trump. They are also exploring possible links between Trump aides and Russian officials.
Former acting attorney general Sally Yates and former director of national intelligence James Clapper are scheduled to testify before a Senate Judiciary subcommittee on May 9. The House Intelligence Committee has also invited Yates and Clapper to testify in a public hearing that has not yet been scheduled.
The House probe in particular has been beset with controversy after the Intelligence Committee's chairman, Republican Devin Nunes, publicly signalled that he had seen information suggesting the identity of Trump or members of his transition team may have been revealed in classified surveillance reports.
The Oversight Committee asked the White House in March for documents pertaining to Flynn's security-clearance applications, the vetting that occurred before he was named national security adviser, and all of his contacts with foreign agents, including any payments received. In particular, the committee heads requested to see a disclosure form known as the SF86, on which Flynn was obligated to declare any foreign income.
On April 20, the White House sent the committee a reply, stating that any documents related to Flynn from before Trump took office were not in its possession and that any documents from after that date did not seem relevant to the committee's investigation.
"The White House has refused to provide this committee with a single piece of paper in response to our bipartisan request," Cummings said.
