“According to public reports, he watched television happily — happily — as the chaos unfolded,” Mr. McConnell said on Saturday. “He kept pressing his scheme to overturn the election. Even after it was clear to any reasonable observer that Vice President Pence was in serious danger, even as the mob carrying Trump banners was beating cops and breaching perimeters, the president sent a further tweet attacking his own vice president.”

Senator Lindsey Graham of South Carolina, a close Republican ally of the president’s, told The Washington Post that he called Ivanka Trump, Mr. Trump’s eldest daughter, to try to get her to reason with her father. Mark Meadows, the White House chief of staff, also called Ms. Trump to see if she could talk to her father. A short time later, she arrived in the Oval Office, urging Mr. Trump to issue a statement.

The White House counsel, Pat A. Cipollone, hammered at Mr. Trump to understand that he had potential legal exposure for what was taking place.