President Trump said he plans to “look into” reports that his national security adviser, Michael T. Flynn, discussed sanctions in his pre-inauguration conversations with Russia’s ambassador to the United States and possibly misled administration officials about it.

“I don’t know about that. I haven’t seen it,” said Mr. Trump, speaking to reporters on Air Force One late Friday, during a flight to Florida from Washington. Several news outlets reported on Thursday that Mr. Flynn and Ambassador Sergei I. Kislyak had discussed sanctions that the Obama administration had imposed on Russia.

The White House has denied publicly that the two men discussed sanctions.

Even as Mr. Trump professed his lack of knowledge of the episode, administration officials were scrambling to contain the fallout of the latest revelations about the embattled former three-star general, who has been criticized internally for his judgment and for staffing the National Security Council with military officers instead of trained civilian personnel.

Perhaps a bigger concern for Mr. Flynn is his relationship with Vice President Mike Pence, who sometimes has had to defend him in public.