However, a spokesman said Cameron acknowledges criticism of the proposed Communications Data Bill in its present form and would rewrite it, the BBC reported Wednesday.
Even Deputy Prime Minister Nick Clegg had threatened to block the legislation barring a "rethink" and demanded a "balance between security and liberty," the BBC reported.
A committee of MPs and peers had criticized the bill's scope, saying it gave "insufficient attention to the duty to respect the right to privacy."
"We recognize this is a difficult issue," Clegg said. "We will take account of what the committee said."
Civil liberties proponents have dubbed the bill a "snoopers' charter," but Home Secretary Theresa May has said such powers are needed in the battle against pedophiles, terrorists and those committing computer crimes.
The draft bill includes a provision that would require Internet service providers to store for a year all details of online communication in Britain, including all Britons' Web-browsing history and details of messages sent on social media, webmail, voice calls over the Internet, emails and phone calls.