Washington: President Donald Trump says he has "nothing to hide" from the special counsel investigating Russian interference in the 2016 US election, and denies that his top lawyer had turned on him by co-operating with the probe.

Trump, in a series of tweets, denounced The New York Times for a Saturday story saying White House Counsel Don McGahn has co-operated extensively with the special counsel, Robert Mueller. The Times said McGahn had shared detailed accounts about the episodes at the heart of the inquiry into whether Trump obstructed justice.

"I allowed him and all others to testify - I didn't have to," Trump said in a tweet on Sunday.

Trump said the newspaper made it seem like McGahn had turned on the president - as White House counsel John Dean had in the Watergate investigation of former president Richard Nixon - "when in fact it is just the opposite".