WASHINGTON -- Sen. Dianne Feinstein, D-California, said Sunday that she believes the ongoing probe into possible collusion between Russia and the Trump campaign now includes the question of a possible cover-up.

"Do you get the sense that the federal investigation into this includes something beyond just the question of Russia and the Trump campaign but that it now includes a cover-up question?" CBS News' John Dickerson asked Feinstein on "Face the Nation."

"Well, I think that's right. It does," said Feinstein, the ranking Democrat on the Senate Intelligence Committee. "I know what the president told me when he called to say that he was firing him. And that turned out not to be the reason."

Feinstein's comments raise more questions about the investigation, which is now being led by former FBI Director Robert Mueller, who was appointed as special counsel to oversee the probe. They also come after a whirlwind week in Washington as reports emerged that Mr. Trump told Russian diplomats that his firing of "nut job" James Comey relieved "great pressure" on him, and that a senior White House adviser is a target of the law enforcement investigation into any ties between Russia and Trump associates.

Before those reports came out, CBS News confirmed reporting by The New York Times that said Mr. Trump asked Comey to end the FBI investigation into former National Security Adviser Michael Flynn and his ties to Russia and Turkey, as detailed in a memo that Comey wrote.

Questions also continue to swirl about what exactly the White House knew about ousted Flynn, after The New York Times reported Wednesday that Flynn had told Mr. Trump's transition team weeks before the presidential inauguration that he was under federal investigation for secretly working as a paid lobbyist for Turkey during the campaign.

The Times' reporting, which cited two people familiar with the case, said that despite Flynn's Jan. 4 disclosure about the investigation to White House counsel Donald McGahn, Mr. Trump brought Flynn onto his team. The report also says that people close to Flynn say he believed that when the warning to Mr. Trump did little to dissuade him from appointing him as national security adviser, the Justice Department then opened its investigation into his lobbying work.

The White House has since denied the report.

Feinstein said Sunday that "the Senate and the House have to feel a sense of stability from day to day."

"We can't feel the anxiety that goes with not knowing what may happen next, what may be said next," she said. "And we need to depend on our president for truth. That is really important."