Cameron, who had dismissed the idea as "divisive, stupid and wrong" when Trump proposed it in December, told a press conference in London that it was clear that "the policy idea that was put forward was wrong".
However, he said the billionaire property tycoon "deserves our respect" for his victory in one of the most contentious and chaotic nomination battles in generations.
In the wake of a shooting by a Muslim couple in San Bernardino, California, that left 14 dead, Trump urged a "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on".
He was responding to a question about a petition signed by more than half a million people calling for Trump to be banned from entering Britain, where Muslims make up about five percent of the population.
A foreign policy advisor to Trump, George Papadopoulos, told The Times this week that the campaign team had been shocked by the British prime minister's comments.
Asked today whether he owed Trump an apology, Cameron told reporters: "It's obviously a matter for the voters in the US to decide who they choose as their next president.
"Knowing the gruelling nature of primaries and what you have to go through, anyone who makes it through that extraordinary contest to lead their party into a general election certainly deserves our respect.
