He made the comments Thursday after Justice Minister Michael Gove -- one of his senior ministers and a leading campaigner for Britain to leave the EU -- denied he was the source of the controversial story.
Buckingham Palace is in a standoff with The Sun
, one of Britain's most powerful newspapers, over a front-page article it published Wednesday headlined, "Queen backs Brexit."
The phrase "Brexit" refers to a potential "British exit" from the European Union. Britons will vote in a national referendum June 23 on whether to leave or stay in the 28-member bloc.
The Sun's report caused a stir in Britain, a constitutional monarchy in which the royal family is traditionally seen as above political matters.
Last month, sections of the British media interpreted remarks by the Queen's grandson Prince William as suggesting Britain would be better off in Europe.
But a spokesman for the prince denied the speech had anything to do with the European question.
Palace complains to press watchdog
The palace issued a statement Wednesday insisting the Queen was neutral on whether the UK should leave the EU, and said a complaint had been made with Britain's press watchdog, the Independent Press Standards Organization, disputing the article's accuracy.
In response, the newspaper insisted it stood by the story, and would defend the complaint "vigorously," according to a spokesman.
Cameron said the press watchdog should be allowed to do its work in investigating the matter, and described Gove's denial as "very clear."
"As far as I can see, Michael Gove has made clear that he has no idea where this story came from," he said.
The report cited an unnamed "senior political source" who claimed that at a 2011 lunch at Windsor Castle, the Queen told Nick Clegg, who was deputy prime minister at the time, that the EU was heading in the wrong direction.
It reported that those present "were left in no doubt about her views on Europe."
Clegg described the story as "nonsense."
The Brexit debate
has been campaigning for the UK to remain in the European Union, arguing that a recent deal giving Britain "special status" within the bloc would let it have "the best of both worlds.
He argues that the British economy will suffer if the country opts out, and that Britain will be stronger and safer if it remains part of the EU.
But high-ranking members of Cameron's Cabinet, including Gove, and Boris Johnson, London's charismatic mayor
and one of the UK's most popular and influential politicians, are campaigning for a "Leave" vote.
They argue that the EU diminishes British sovereignty, brings too much red tape and has led to excessive immigration.
Perhaps reflecting its island geography, Britain has always been more ambivalent towards the union than its fellow members.
It opted to remain outside the Schengen Agreement, which allows passport-free travel among most European countries, and kept the pound as its currency when others adopted the euro.
Polls show the British public torn on the question. A recent poll by YouGov
found 40% in favor of staying in the bloc and 37% support for leaving.