A police investigation was later launched after CCTV footage appeared to suggest the claims were incorrect.
While the Prime Minister declined to discuss the ongoing police inquiry, he made a point of praising Mr Mitchell, saying he was a "very talented politician".
He added: "We have to wait for the outcome and then make decisions.
"I have enormous respect for him. He was a brilliant Development Secretary. I am very sorry about all the things that have taken place. We have to let this investigation take place and then we can take it from there."