President Trump said Saturday that he gave White House counsel Don McGahn permission to cooperate extensively with the special counsel’s investigation into Russian interference in the U.S. election, following a news report detailing the extent of Mr. McGahn’s interactions.

“I allowed White House Counsel Don McGahn, and all other requested members of the White House Staff, to fully cooperate with the Special Counsel,” Mr. Trump wrote in a tweet Saturday, while spending the weekend at his golf resort in Bedminster, N.J. “In...