- "I think the best way for our country.... is for the president to resign and go away as soon as possible," Sen Toomey told NBC's Meet the Press.
The US House of Representatives could vote as early as Tuesday on an article of impeachment against President Donald Trump, a senior Democrat has said.
House Democrats plan to introduce a charge of “incitement of insurrection” against the president over his role in the violent storming of the Capitol.
House whip James Clyburn told CNN action would be taken this week.
But the party may not send any articles to the Senate for trial until after Joe Biden’s first 100 days in office.
“Let’s give President-elect Biden the 100 days he needs to get his agenda off and running,” Mr Clyburn said.
That would allow Mr Biden to confirm his new cabinet and kick-start key policies including tackling coronavirus – something that would have to wait if the Senate had already received the impeachment articles.
Mr Trump has made no public statements since he was banned from several social media platforms – including Twitter – on Friday.
On Sunday, however, the White House announced that the president will travel to Texas on Tuesday to visit a stretch of the border wall with Mexico to highlight his administration’s work there.
Mr Trump has been accused by Democrats and an increasing number of Republicans of encouraging last Wednesday’s riot in Congress in which five people died.
But no Republican senators have said they will vote to convict him of wrongdoing in the Senate.
A second Republican senator, Pat Toomey, called for Mr Trump to resign on Sunday.
“I think the best way for our country…. is for the president to resign and go away as soon as possible,” Sen Toomey told NBC’s Meet the Press.
“I acknowledge that may not be likely, but I think that would be best.”