WASHINGTON — President Trump indirectly criticized Robert S. Mueller III, the special counsel, on Wednesday for the continuing investigation into Russia’s 2016 campaign meddling, even as a former C.I.A. director said during a morning news show that President Vladimir V. Putin of Russia may have compromising information on Mr. Trump.

After a weekend of attacking Mr. Mueller — against the advice of his own lawyers — Mr. Trump picked up again in early morning tweets when he said he was quoting a former Harvard professor stating that Mr. Mueller should never have been appointed to be the special counsel to investigate Russia’s meddling in the 2016 election. That investigation has expanded into inquiries into Mr. Trump’s aides and his own business dealings.

“I was opposed to the selection of Mueller to be Special Council,” Mr. Trump wrote in a Twitter post that he attributed to a professor emeritus at Harvard Law School, Alan M. Dershowitz.