Cameron, who had met in Washington with President Barack Obama on Wednesday, earlier dropped in on the mayor of Newark, a city near New York where the mayor is dealing with major budget challenges and reforms to the schools system.
In New York, Cameron and his wife Samantha paid tribute to the nearly 3,000 people killed on September 11, 2001 when hijacked airliners destroyed the World Trade Center.
He then did a question-and-answer session with New York University students, joking that they must be "the most devoted" because they had come to the event during the Spring break holiday.
Cameron fielded questions on heavyweight issues from the international field of students, ranging from Iran's nuclear ambitions to moves in Scotland toward independence from Britain.
While supporting a muscular foreign policy as a close US ally, Cameron warned against "grand plans and schemes to remake the world."
On the future of the Falkland Islands, where Britain went to war 30 years ago to drive out an Argentine occupying force, Cameron reassured a woman in the audience that she need not fear a new split in her household, where her husband is from Argentina.
"I don't think you do," he said, insisting that his policy was based entirely on the desire of the island residents to remain under British rule.
"That is not going to change," he said. "I knew there was going to be a lot of noise and diplomatic activity (on the anniversary)."
Cameron said the London Olympics were ready to start, with a "glistening Olympic park."
His biggest excitement, though, he joked was "if I stand on the roof of Number 10 Downing Street, I can look down on Horse Guards Parade, which is where they have the beach volleyball."
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