Senate Majority Leader Mitch McConnell and other senior figures in Mr Trump’s Republican Party had no hesitation in committing to an orderly transfer if Trump loses.
The president, responding to a question about committing to the results, said on Wednesday that “we’re going to have to see what happens”.
He added: “You know that I’ve been complaining very strongly about the ballots and the ballots are a disaster.”
Mr McConnell responded in a tweet: “The winner of the November 3 election will be inaugurated on January 20.
“There will be an orderly transition just as there has been every four years since 1792.”
Democrat House Speaker Nancy Pelosi said it was “very sad” the president of the US was even raising this question.
She asked “What would our founders think?
“Calm down, Mr President.”
She reminded Mr Trump the US is not North Korea, Russia, Saudi Arabia or other countries with strongman leaders he openly admires.
“You are in the United States of America, it is a democracy,” she said.
“So why don’t you just try for a moment to honour our oath of office to the constitution of the United States?”
Ms Pelosi said she has confidence in American voters to cast their votes and choose the president.
Hardly any Republican politicians came to the president’s defence.
Senator Lindsey Graham, an ally of Mr Trump and chairman of the Senate Judiciary Committee, told Fox & Friends on Thursday: “If Republicans lose we will accept the result.
“If the Supreme Court rules in favour of Joe Biden, I will accept that result.”
Congresswoman Liz Cheney, of Wyoming, a member of the House GOP leadership, tweeted: “The peaceful transfer of power is enshrined in our Constitution and fundamental to the survival of our Republic.
“America’s leaders swear an oath to the Constitution. We will uphold that oath.”
Long-time senator Richard Shelby, of Alabama, chairman of the Appropriations Committee, said: “Well, we’ve always had a peaceful transfer of power. That’s one of the hallmarks.
“And I think this year will be no exception.”
It is highly unusual that a sitting president would express less than complete confidence in the electoral process.
But Mr Trump also declined four years ago to commit to honouring the election results if his Democratic opponent, Hillary Clinton, won.
Mr Biden, his current Democratic challenger, was asked about Trump’s comment after landing in Wilmington, Delaware, on Wednesday night.
“What country are we in?” Mr Biden asked incredulously, adding: “I’m being facetious. Look, he says the most irrational things.
“I don’t know what to say about it. But it doesn’t surprise me.”
Mr Trump has been pressing a months-long campaign against mail-in voting this November by tweeting and speaking out critically about the practice.
More states are encouraging mail-in voting to keep voters safe during the coronavirus pandemic.
Fundamental to democracy is the peaceful transition of power; without that, there is Belarus. Any suggestion that a president might not respect this Constitutional guarantee is both unthinkable and unacceptable.
— Mitt Romney (@MittRomney) September 24, 2020
The president, who uses mail-in voting himself, has tried to distinguish between states that automatically send mail ballots to all registered voters and those, like Florida, that send them only to voters who request a mail ballot.
Mr Trump has claimed widespread mail voting will lead to massive fraud but the five states that routinely send mail ballots to all voters have seen no significant fraud.
Ohio Congressman Steve Stivers, a former chairman of the House Republican campaign arm, tweeted: “Regardless of how divided our country is right now, when elections are over and winners are declared, we must all commit ourselves to the constitution and accept the results.”
Senator Mitt Romney, one of the lone GOP voices to cross Mr Trump, referred to an electoral crisis in Europe, tweeting: “Fundamental to democracy is the peaceful transition of power; without that, there is Belarus.
“Any suggestion that a president might not respect this Constitutional guarantee is both unthinkable and unacceptable.”
