BERKELEY HEIGHTS, N.J. — President Trump attacked The New York Times on Sunday in a series of tweets in which he denounced a report describing the extensive cooperation between the White House counsel, Donald F. McGahn II, and the special counsel’s investigators.

In the Twitter posts, the president confirmed that he had made the unusual decision to allow Mr. McGahn and other officials to cooperate fully with the inquiry, saying he had “nothing to hide.” But Mr. Trump said the Times article had falsely insinuated that Mr. McGahn had “turned” on him.

“The failing @nytimes wrote a Fake piece today implying that because White House Councel Don McGahn was giving hours of testimony to the Special Councel, he must be a John Dean type ‘RAT,’” Mr. Trump said, referring to the Nixon White House counsel who cooperated with investigators in the Watergate investigation.