WASHINGTON—Leaders of the House Oversight Committee said former national security adviser Mike Flynn may have violated the law by failing to obtain required permission from the Army and State Department before receiving money from entities associated with the Russian and Turkish governments.

Mr. Flynn also failed to disclose payments from a Russian state television network when he renewed his security clearance last year, as was required, one of the committee leaders said.

The panel’s Republican chairman, Rep. Jason Chaffetz of Utah, and Democratic ranking member, Rep. Elijah Cummings of Maryland, said they are asking the Defense Department to determine whether Mr. Flynn, a former three-star Army general and head of the military’s Defense Intelligence Agency, must return payments he received after leaving the military for work linked to foreign governments.

“I see no information or no data to support the notion that Gen. Flynn complied with the law,” said Mr. Chaffetz in a joint news conference with his Democratic counterpart at the U.S. Capitol on Tuesday, after viewing classified documents provided by the Defense Department.

The documents were given to the committee as part of its investigation into the circumstances surrounding Mr. Flynn’s departure from President Donald Trump’s administration.