WASHINGTON — The Democratic-led House Intelligence Committee said on Thursday that it had issued two new subpoenas demanding that Michael T. Flynn, President Trump’s former national security adviser, and Rick Gates, a former top Trump campaign aide, provide testimony and documents related to their interactions with Russians and other foreign powers.

The subpoenas, dated Wednesday, are tied to the Intelligence Committee’s investigation of Russia’s attempts to influence the American political system and whether Russia or other foreign interests could have influence over Mr. Trump, his family or associates.

Mr. Flynn and Mr. Gates played key roles providing information and testimony to Robert S. Mueller III, the special counsel who investigated Russia’s 2016 election influence campaign, and could boost efforts by House Democrats to raise the profile of Mr. Mueller’s conclusions with the public if they cooperate.

Representative Adam B. Schiff of California, the Intelligence Committee’s chairman, said Thursday that the subpoenas were necessary because Mr. Flynn and Mr. Gates had so far refused to fully cooperate with the committee voluntarily.