The third most senior Republican in the House of Representatives, Liz Cheney, said Mr Trump "lit the flame" of the attack that resulted in five deaths.
A vote in the Democratic-controlled House is expected on Wednesday.
In his first public appearance since the riot, the president took no responsibility for the violence.
Democrats accuse Mr Trump of encouraging his supporters to storm the Capitol building. They are expected to push for a vote to impeach Mr Trump, to formally charge him with inciting insurrection.
Will Trump be impeached? As Democrats hold a majority in the House, the vote is likely to pass. The case will then head for the Senate, where a trial will be held to determine the president's guilt.
A two-thirds majority would be needed to convict Mr Trump, meaning at least 17 Republicans would have to vote for conviction. As many as 20 Senate Republicans were open to convicting the president, the New York Times reported.
The timeline of when a trial could be held is not known but it is unlikely it could be finished before Mr Trump leaves office on 20 January, when Joe Biden will be sworn in as president.
The Senate could also use an impeachment trial to hold a vote blocking Mr Trump from ever running for office again. He has indicated he plans to campaign for president in 2024.
Can Trump be removed or banned from politics? How many arrests so far from Capitol riots? FBI fears armed protests ahead of Biden's inauguration Wednesday's vote means that Mr Trump is likely to become the first US president ever to be impeached twice.
He became the third president to be impeached in December 2019 over charges of breaking the law by asking Ukraine to investigate Mr Biden in the election. The Senate cleared him at a trial.
What have Republicans said? Ms Cheney, the daughter of former Vice-President Dick Cheney, vowed to back impeachment, saying Mr Trump had "summoned this mob, assembled the mob, and lit the flame of this attack".
"There has never been a greater betrayal by a president of the United States of his office and his oath to the Constitution," the Wyoming representative added.
Three other Republican House members - John Katko, Adam Kinzinger and Fred Upton - said they would also vote for impeachment.
House Republican leader Kevin McCarthy, a Trump ally who has said he opposes impeachment, decided not to ask rank-and-file members of the party to vote against the measure, US media reported.
According to the New York Times, Senate Republican leader Mitch McConnell told confidants he was pleased Democrats wanted to impeach the president because he believed it would help rid the Republican party of Mr Trump.
n the time it took Air Force One to fly Donald Trump back from the Texas border on Tuesday, the political ground crumbled beneath his feet. Mitch McConnell's signals that he is "pleased" with Democratic efforts suggest the political calculus is changing for Republican leaders in Congress.
A growing number believe the unrepentant president's actions last week threatened not just US democracy, but also their personal safety.
And even before the riot at the US Capitol, Mr Trump was increasingly viewed as a political liability with dwindling power. His scorched-earth challenge to the election results probably cost Republicans two Senate seats in Georgia, and there has been scant proof that Mr Trump boosts the party's electoral chances when his name is not on the ballot.
Mr McConnell, among others, may be mulling whether a clean break with Trump is better for their political futures, even if it means working with Democrats to do the job.
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