Calls for Osborne's departure increased after the Office of National Statistics reported the national economy shrank .7 percent between April and June, The Guardian reported.
Cameron, in an interview with Sky News, said the chancellor, who is also in charge of Conservative election strategy, will be in the Cabinet at the 2015 election and "is not going anywhere."
"George Osborne is doing an excellent job in very difficult circumstances and he has my full support in going on and doing that job," Cameron said.
Cameron is believed to be planning a cabinet reshuffle in the fall.
Asked about Jeremy Hunt, the minister for culture, media and sport, Cameron gave no guarantee. Hunt has been under fire because of revelations that he communicated privately with James Murdoch while he was to decide whether the Murdoch family's News Corp. would be able to acquire BSkyB.
"If you're going to try and go through sort of, reshuffle bingo I'm going to leave it at that," Cameron said, while praising Hunt's work on Olympic security.