WASHINGTON — Attorney General Jeff Sessions faced growing pressure on Tuesday to remove himself from any role in investigating President Trump’s aides and their relationship with Russia, but advisers to Mr. Sessions said he saw no need to do so.

The resignation of Michael T. Flynn as national security adviser over his conversations with the Russian ambassador gave new impetus to demands from Democrats and outside groups who say Mr. Sessions lacks the independence to oversee criminal investigations that might lead back to the White House. He and Mr. Flynn were both early and influential advisers in Mr. Trump’s presidential campaign.

Senator Chuck Schumer of New York, the Democratic leader, said Tuesday that under the Justice Department’s guidelines on possible conflicts, that personal history should “disqualify” Mr. Sessions from overseeing any investigations.

And Senator Patrick J. Leahy, a Vermont Democrat who sits on the Judiciary Committee, said in an interview Tuesday that if Mr. Sessions failed to ensure that there would be no political interference, “then of course he has to have someone from the outside come in.”