Andy Coulson, former News of the World editor, arrested in hacking scandal
Cameron also suggested that a decision on Murdoch's BSkyB takeover is likely to be delayed.
"Given the events of recent days, this will take some time," Cameron said.
The prime minister refused to apologize for hiring Coulson as his spokesman, a move that opposition Labour Party leader Ed Miliband described Friday as an "appalling error of judgment."
Cameron said Coulson, who resigned from his government post in January, remained a friend.
The prime minister referred to reports that Brooks had offered her resignation. "In this situation I would have taken it," Cameron said.
A reporter asked whether James Murdoch was a fit and proper person to run a company, following his admission on Thursday that regretted authorizing out-of-court payments to some hacking victims.
Murdoch's statement "raises lots of questions that need to be answered," Cameron said.
The scandal exploded this week after it was reported that the News of the World had hacked the mobile phone of 13-year-old murder victim Milly Dowler in 2002 while her family and police were desperately searching for her. News of the World operatives reportedly deleted some messages from the phone's voicemail, giving the girl's parents false hope that she was still alive.
That ignited public outrage far beyond any previous reaction to press intrusion into the lives of celebrities, which the paper had previously acknowledged and for which it paid compensation.
Dozens of companies pulled their advertising from the paper this week, fearing they would be tainted by association. James Murdoch then announced Thursday that this Sunday's edition of the tabloid would be its last and all revenue from the final issue, which will carry no ads, would go to "good causes."
News International, the British unit of Murdoch's News Corp., has not said whether it will move quickly to put another paper into the Sunday market which had been dominated for decades by News of the World. But according to online records, an unnamed U.K. individual on Tuesday bought up the rights to the domain name "sunonsunday.co.uk."
Shares in BSkyB, which have fallen all week because of doubts whether the takeover will go ahead, were down more than 4 percent Friday in London trading at 779 pence ($12.40).
Shares in News Corp. rose 1.6 percent on the Nasdaq index in New York after Thursday's announcement.
The British government on June 30 already gave its qualified approval allowing News Corp. to purchase the 61 percent of British Sky Broadcasting that it doesn't already own, on the condition it spins off Sky News as a separate company. News Corp. made an initial offer of 700 pence per share, valuing BSkyB at 12.3 billion pounds ($19.8 billion). Analysts believe News Corp. may have to go as high as 900 pence per share to persuade shareholders to sell out.
Analyst expect the BSkyB deal approval to be delayed now until at least September.
Despite the public outcry, many analysts think Britain will still sanction the takeover, since officials have already said that threats to competition will be resolved with Sky News' spin-off.
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