Democratic Senator Chuck Schumer said Mr Trump should be removed immediately. If he is not, House Speaker Nancy Pelosi says he could be impeached.
Four people died during the riot, and 68 have now been arrested.
Police have faced criticism for failing to stop the rioters breaking in.
The official responsible for the security in the House of Representatives, the sergeant at arms, has now resigned. Mr Schumer has called for his counterpart in the Senate to be sacked.
President-elect Joe Biden said: "Nobody could tell me that if it was a group of Black Lives Matter protesters yesterday they wouldn't have been treated very differently than the thugs that stormed the Capitol."
The head of the US Capitol Police (USCP) said his officers had faced "criminal riotous behaviour" and he described officers' actions as "heroic".
Ms Pelosi, however, has called on him to resign.
Transport Secretary Elaine Chao is the latest member of the Trump administration to quit in protest over the riots. Several lower-level officials have also resigned.