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.