WASHINGTON — President Trump indirectly criticized Robert S. Mueller III, the special counsel, on Wednesday for the ongoing 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 quoted a Harvard professor who said 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 tweeted, misspelling the word, “counsel,” as he quoted Alan M. Dershowitz, a Harvard Law professor who has been outspoken in his defense of the president.

 

Separately, on MSNBC’s “Morning Joe,” John O. Brennan, a former C.I.A. director, speculated that the Russians “may have something on him personally,” referring to Mr. Trump.

Mr. Brennan was the C.I.A. director when a salacious dossier surfaced in 2016 that claimed the Russians had compromising information on Mr. Trump. There has been no proof that such material exists, but Mr. Trump’s affection for the Russian leader has raised questions about the nature of their relationship.

On Tuesday, Mr. Trump congratulated Mr. Putin on his re-election and made no mention of the election meddling. Mr. Trump has routinely issued statements about Russia and Mr. Putin that sound at odds with his own advisers and administration actions.

“I think he’s afraid of the president of Russia,” said Mr. Brennan, now retired from government service and a critic of Mr. Trump.

On Saturday, Mr. Brennan attacked Mr. Trump on Twitter after the president tweeted about his excitement over the firing of the deputy director of the F.B.I., Andrew G. McCabe.

“When the full extent of your venality, moral turpitude, and political corruption becomes known, you will take your rightful place as a disgraced demagogue in the dustbin of history,” Mr. Brennan wrote.

For months, Mr. Trump personally attacked Mr. McCabe, a 21-year veteran of the F.B.I. and former deputy director. Mr. McCabe briefly served in the top role after Mr. Trump fired James B. Comey, the president’s first F.B.I. director. Mr. McCabe was fired on the eve of his retirement, which puts his government pension in jeopardy. After the firing, it was disclosed that Mr. McCabe kept memos on Mr. Trump, which Mr. Mueller’s investigators can access.

Mr. Mueller has accused 13 Russians and three companies of election meddling. Three of Mr. Trump’s former associates have pleaded guilty as part of the ongoing inquiry. Last week, the special counsel issued subpoenasfor the Trump organization, seeking documents including some related to Russia.

Mr. Trump has consistently called the investigation into Russia’s meddling a “hoax.”

“I think President Trump was right when he said there never should have been a Special Council appointed,” Mr. Trump quoted Mr. Dershowitz as saying.