The White House has insisted Donald Trump will accept the result of a "free and fair" election.
It followed outrage over his refusal to commit to a peaceful transfer of power.
At a press conference yesterday, President Trump said: "We'll have to wait and see" - citing his repeated, false claims that mail-in ballots being vulnerable to fraud.
Earlier, the President had been jeered with chants of "vote him out" as he visited the US Supreme Court, where the late Justice Ruth Bader Ginsberg is lying in state.
His remarks led to Senate Republican Leader Mitch McConnell joined other Republican lawmakers in rallying to the defense of constitutional government.
"The winner of the November 3rd election will be inaugurated on January 20th. There will be an orderly transition just as there has been every four years since 1792," McConnell wrote in a tweet.
"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," Representative Liz Cheney, who leads the House of Representatives Republican Conference, wrote on Twitter.
But not all Republicans expressed alarm at Trump's remarks.
"In the spring, stores sold out of hand sanitizer and toilet paper. This fall, they sold out of ammo," tweeted Representative Thomas Massie, a member of the conservative House Freedom Caucus.
The former vice president's campaign said it was prepared for any "shenanigans" from Trump, and reiterated comments from July that "the United States government is perfectly capable of escorting trespassers out of the White House."