Republican leader Mitch McConnell has said there will be an “orderly” post-election transition after the president questioned the process’ integrity.
The top US senator said regardless of who wins the 3 November presidential election, there will be a peaceful inauguration on 20 January.
A day earlier, President Donald Trump refused to commit to this, saying “we’ll have to see what happens”.
He has cast doubt on postal voting, but election officials insist it is safe.
The president currently trails his challenger, Democrat Joe Biden, in national opinion polls with 40 days to go until the election.
Many more Americans than usual will be casting their votes by post this year, due to the pandemic, and Mr Trump has been questioning the security of this mail-in ballot system.
Every losing presidential candidate has conceded. If Mr Trump were to refuse to accept the result of the election, it would take the country into uncharted territory.
Mr Biden has suggested that should this happen, the military could remove Mr Trump from the White House.
What have Republicans said?
“The winner of the November 3rd election will be inaugurated on January 20th,” Mr McConnell tweeted on Thursday.
“There will be an orderly transition just as there has been every four years since 1792.”
Other Republican lawmakers, including vocal Trump ally Senator Lindsey Graham, have similarly promised a safe and fair election.
“I can assure you it will be peaceful,” Mr Graham told Fox News.
Senator Mitt Romney offered a more critical response on Wednesday, saying “any suggestion that a president might not respect this Constitutional guarantee is both unthinkable and unacceptable”.
What did Trump say?
Mr Trump was asked by a reporter on Wednesday evening if he would commit to a peaceful transfer of power “win, lose or draw” to Mr Biden.
“I’ve been complaining very strongly about the ballots,” Mr Trump said. “And the ballots are a disaster.”
When the journalist countered that “people are rioting”, Mr Trump interjected: “Get rid of the ballots, and you’ll have a very – you’ll have a very peaceful – there won’t be a transfer, frankly, there’ll be a continuation.”