Trump’s refusal to commit to accepting the results of November’s election — something no other modern president has put in doubt — led several prominent Republicans, including Senator Mitch McConnell of Kentucky, the majority leader, to insist Thursday that there would be a peaceful transfer of power come January.

“The winner of the November 3rd election will be inaugurated on January 20th,” Mr. McConnell wrote on Twitter. “There will be an orderly transition just as there has been every four years since 1792.”

Trump also went on to question the integrity of “the ballots” — apparently referring to mail-in voting, which he has falsely called rife with fraud — and added that if he were able to “get rid of” the ballots and ensure a “continuation” rather than a “transfer,” it would be peaceful.

The peaceful transfer of power and accepting election results are fundamentals of democracy.

Many Republicans, including McConnell, distanced themselves from the remarks and insisted that there would be a peaceful transfer of power if Biden wins the presidency.

Senator Dan Sullivan, Republican of Alaska, declaired, “of course we’re going to have a peaceful transition of power. We’re the United States of America. We’re not a banana republic.”

“I don’t know what his thinking was, but we have always had a controlled transition between administrations,” said Senator Susan Collins, Republican of Maine. She said “the peaceful transfer of power is a fundamental tenet of our democracy, and I am confident that we will see it occur once again.”

Senator Lindsey Graham, Republican of South Carolina said, “People wonder about the peaceful transfer of power,” he said. “I can assure you, it will be peaceful.” He added, “I promise you as a Republican, if Joe Biden wins, I will accept the result. If Republicans lose, we’ll accept the result.”