Cameron said in London, "When (Coulson) was editor of the News of the World, bad things happened at that newspaper. I gave him a second chance."
The BBC and the British Guardian reported Coulson said the allegations regarding the bugging of celebrities' phones during his tenure as editor of the News of the World are making it more difficult for him to perform his work as press secretary.
Cameron and Chancellor George Osborne, however, refused Coulson's resignation offer, instead offering their complete support as Coulson tries to clear his name, The Guardian reported.
In 2007, Coulson resigned as editor of the News of the World over the bugging incident, but has always said he was unaware of it at the time, the Guardian reported.
"I judge his work by what he has done for us. ... He resigned for what went wrong at News of the World," Cameron said.