Senior Trump administration officials have pushed American spy agencies to hunt for evidence to support an unsubstantiated theory that a government laboratory in Wuhan, China, was the origin of the coronavirus outbreak, according to current and former American officials. The effort comes as President Trump escalates a public campaign to blame China for the pandemic.

Robert S. Mueller III revealed a frantic, monthslong effort by President Trump to thwart the investigation into Russia’s 2016 election interference, cataloging in a report released on Thursday the attempts by Mr. Trump to escape an inquiry that imperiled his presidency from the start.

As federal prosecutors in Manhattan gathered evidence late last year about President Trump’s role in silencing women with hush payments during the 2016 campaign, Mr. Trump called Matthew G. Whitaker, his newly installed attorney general, with a question. He asked whether Geoffrey S. Berman, the United States attorney for the Southern District of New York and a Trump ally, could be put in charge of the widening investigation, according to several American officials with direct knowledge of the call.

An adviser to the United Arab Emirates with ties to current and former aides to President Trump is cooperating with the special counsel, Robert S. Mueller III, and gave testimony last week to a grand jury, according to two people familiar with the matter. Mr. Mueller appears to be examining the influence of foreign money on Mr. Trump’s political activities and has asked witnesses about the possibility that the adviser, George Nader, funneled money from the Emirates to the president’s political efforts.

A former top adviser to Donald J. Trump’s presidential campaign pleaded guilty on Friday to fraud and lying to investigators in the special counsel inquiry into Russia’s interference in the 2016 election and will cooperate with the investigation.