There has been tension between the White House and the inquiry and President Trump has had to deny planning to fire lead investigator Robert Mueller.
The president again denied there had been any collusion with Russian officials.
He said he did not know how long the inquiry would take, but it had made the US “look very bad”.
The interview took place at the president’s golf club in West Palm Beach in Florida.
President Trump insisted he had the right to begin or end any justice department investigations.
He said of Robert Mueller, the special counsel: “I think he’s going to be fair.”
According to the New York Times, President Trump had denied 16 times during the interview that there had been any collusion with Russia.
US intelligence agencies believe Russia tried to tip the presidential election in favor of Donald Trump – a charge denied by both Moscow and the president.
The president has labeled Robert Mueller’s investigation a “witch hunt” while other Republicans accuse it of bias.
Donald Trump repeated his allegation that Democrats had invented the issue “as a hoax, as a ruse, as an excuse for losing an election”.
He said he was not concerned about when the inquiry would finish as he had nothing to hide.
However, the president added: “It makes the country look very bad, and it puts the country in a very bad position. So the sooner it’s worked out, the better it is for the country.”
He repeated his comments from May that the investigation was “hunting the US terribly”.
President Trump said the matter had angered his supporters, adding: “My base is stronger than it’s ever been.”
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