WASHINGTON—In the weeks before President Donald Trump fired FBI Director James Comey, a federal investigation into potential collusion between Trump associates and the Russian government was heating up, as Mr. Comey became increasingly occupied with the probe.

Mr. Comey started receiving daily instead of weekly updates on the investigation, beginning at least three weeks ago, according to people with knowledge of the matter and the progress of the Federal Bureau of Investigation probe. Mr. Comey was concerned by information showing possible evidence of collusion, according to these people.

White House officials said Wednesday that Mr. Trump had for months been contemplating the possibility of removing Mr. Comey, and that the dismissal this week wasn’t connected to the Russian probe.

Meanwhile, a congressional investigation into Russian meddling picked up steam as the Senate Intelligence Committee issued a subpoena Wednesday for the president’s former national security adviser, Mike Flynn, to produce documents relevant to the investigation. And a federal grand jury in Northern Virginia has issued subpoenas for records tied to Mr. Flynn, according to a person familiar with the matter.

FBI and Senate investigations into Mr. Flynn, which had been looking into the nature of his contacts with Russia before he joined the White House, expanded in recent weeks to include an examination of Mr. Flynn’s tenure as Mr. Trump’s chief security adviser, people familiar with the probe said.