President Donald Trump said Friday, "I don't want to be set up with a perjury trap" by special counsel Robert Mueller, the prosecutor who is investigating possible obstruction of justice by the president.

But Trump also said he is willing to sit down for an interview with Mueller — who also is probing Russian interference in the 2016 presidential election — "under certain circumstances."

Trump's comments aboard Air Force One came a day after his lawyer, Rudy Giuliani, gave conflicting comments about whether Trump would answer certain questions from Mueller. Trump has repeatedly called Mueller's investigation a "witch hunt."

The president referred to the fate of former campaign advisor George Papadopoulos, who is scheduled to be sentenced later Friday for lying to federal authorities in the Russia investigation.

"They got him on, I guess a couple of lies," Trump noted. He then added that former national security advisor Michael Flynn, who likewise has pleaded guilty in Mueller's probe to making false statements, "said he didn't lie, but Mueller's people said he did lie."

"So I don't want to be set up with a perjury trap, No. 1," Trump said. "No. 2, there was no obstruction and there was no collusion."

Giuliani told The Associated Press on Thursday that Trump would refuse to answer questions about obstruction of justice, either in person or in writing.

Mueller is looking at whether the president obstructed justice in the Russia investigation by firing FBI Director James Comey last year, and by criticizing his own attorney general, Jeff Sessions, who recused himself from the case in early 2017. Mueller was appointed special counsel after both Sessions' decision and Comey's firing.

"That's a no-go. That is not going to happen," said Giuliani, who was a federal prosecutor before becoming mayor of New York. "There will be no questions at all on obstruction."

But shortly after the AP ran its story on that ostensibly hard line, Giuliani told NBC News that such questions are "not ruled in or out."

"We have said we would agree to written questions on Russia after we review questions but no further commitment on interviews," Giuliani told NBC News. "After we finish this we will assess it with no agreement to any post-presidential questions."

A spokesman for Mueller declined to comment when contacted by CNBC.