In the latest sign of defiance, the president’s senior cabinet secretary fueled concerns on Tuesday that Mr. Trump would resist handing over power to President-elect Joseph R. Biden Jr. after legal challenges to the vote. “There will be a smooth transition to a second Trump administration,” Secretary of State Mike Pompeo said.

Mr. Trump’s attorney general has at the same time authorized investigations into supposed vote fraud, his general services administrator has refused to give Mr. Biden’s team access to transition offices and resources guaranteed under law and the White House is preparing a budget for next year as if Mr. Trump will be around to present it.

The president has also embarked on a shake-up of his administration, firing Defense Secretary Mark T. Esper as well as the heads of three other agencies while installing loyalists in key positions at the National Security Agency and the Pentagon. Allies expect more to come, including the possible dismissals of the directors of the F.B.I. and the C.I.A…

The standoff left the United States in the position of the kind of country whose weak democratic processes it often criticizes.