Chairman Adam Schiff said that the committee is examining "deep counterintelligence concerns" raised in Mueller's investigative report, a redacted version of which was made public and to Congress in April.
Flynn and Gates were "critical witnesses" for Mueller's investigation, but so far have refused to cooperate fully with Congress, the California Democrat said.
A retired U.S. Army lieutenant general, Flynn admitted lying to federal investigators about his conversations with the Russian ambassador to the United States and cooperated with Mueller for the Russia investigation.
Gates pleaded guilty to conspiracy and false statement charges related to Ukrainian lobbying and political consulting work he did with Paul Manafort, former Trump campaign chair, who has been sentenced to more than seven years in prison.
Mueller concluded his 22-month investigation in March by submitting a report to Attorney General William Barr.
The report stated that there was no evidence that Trump's campaign conspired with the Russian government during the 2016 U.S. presidential election but didn't conclude if the president had obstructed justice.
Instead, Mueller recounted 10 episodes involving Trump and discussed potential legal theories for connecting these actions to elements of an obstruction offense.
It was the Department of Justice that concluded that the Mueller did not have "sufficient" evidence to support a charge in the obstruction case, a move that has drawn scrutiny from Democrats.