“It started with the president talking about how some of the legal scholarship that had been done, saying under the 12th Amendment, the vice president has the ultimate authority to reject invalid electoral votes and he asked me what I thought about it,” Mr. Eastman said.

“It’s a little bit more complicated than that, that’s certainly one of the arguments that’s been put out there, it’s never been tested,” Mr. Eastman said he replied.

Mr. Eastman said that Mr. Pence then turned to him and asked, “Do you think I have such power?”

Mr. Eastman said he told Mr. Pence that he might have the power, but that it would be foolish for him to exercise it until state legislatures certified a new set of electors for Mr. Trump — something that had not happened.

A person close to Mr. Pence, who was not authorized to speak publicly about the Oval Office conversation, said that Mr. Eastman acknowledged that the vice president most likely did not have that power, at which point Mr. Pence turned to Mr. Trump and said, “Did you hear that, Mr. President?”