President Trump's written responses to questions from special counsel Robert Mueller are "likely to be turned over in the next couple of days," Trump attorney Rudy Giuliani told CBS News' Pat Milton in New York.

Mr. Trump told reporters on Saturday he had "very easily" answered Mueller's questions, and would likely submit them the following week. The president's personal legal team has been negotiating back and forth with Mueller's team over questions for weeks, and the completion of them enters into a new phase of Mueller's probe. Mr. Trump insisted that he wrote the answers himself.

"My lawyers don't write answers. I write answers," the president said Friday.

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While the president hasn't completely ruled out a sit-down interview with Mueller, that is looking less likely.

Senior counselor to the president Kellyanne Conway told reporters Monday the president is "not afraid" to sit down with Mueller, but doesn't think that's necessary now.

"His attorneys have I guess counseled him that he should submit those answers in writing and he has. But he's not afraid to sit down just doesn't seem necessary, doesn't rise to that level," Conway said.

Meanwhile, the president continues to call Mueller's investigation a "witch hunt." That investigation has once again come into focus amid Mr. Trump's appointment of the controversial Acting Attorney General Matt Whitaker. Whitaker, who now oversees the Mueller investigation, has been critical of it in the past. Mr. Trump told Fox News' Chris Wallace in an interview that aired Sunday he would not intervene if Whitaker attempts to curtail the investigation.

"I would not get involved," Mr. Trump said. "And all these people that say I'm going to end the investigation, you know, they've been saying that now for -- how long has this witch hunt gone on? It's gone on for, what?"