Opposition Labour politicians have questioned Cameron’s judgment in appointing Andy Coulson to a key media role after he quit as editor of the News of the World tabloid in 2007 when one of the paper’s reporters was jailed for secretly listening to mobile phone messages of royal household staff.

Cameron said Coulson was embarrassed by continuing speculation about what went on at the newspaper while he was in charge, but declined to comment on reports that Coulson had offered to resign from his government role.

A report in the Mail on Sunday newspaper at the weekend said the communications director had apologized to the prime minister and offered to resign for any possible damage he had caused. The report said both Cameron and finance minister George Osborne had rejected his offer and had given him their total support.

Coulson denies being aware of any wrongdoing at the paper, part of Rupert Murdoch’s News Corp media group, and police said last month there was not enough evidence to charge him with any crime.

“Obviously when he was editor of the News of the World, bad things happened at that newspaper and when he found about those, he resigned. That was the right thing to do,” Cameron told BBC Radio 4’s Today program.

“I gave him a second chance,” Cameron added. “I think he has done a good job for the government and for the country.”

The row comes at a sensitive time for News Corp, which is waiting to hear if the British government will clear its planned $12 billion buyout of pay TV operator BSkyB or refer the deal to competition authorities for further investigation.

Losing Coulson would be a blow to the prime minister. The former newspaper editor operates largely behind the scenes but is seen as effective in helping the government to get its message across at a time of tension over cost-cutting measures.

The long-running hacking story flared back into life earlier this month when the News of the World suspended senior editor Ian Edmondson, named in documents uncovered in a lawsuit by film star Sienna Miller, who accuses the paper of breaking into her voice-mail account to hear her messages.

British prosecutors said last week they would re-examine all material police held on alleged phone hacking.