Asked about the alleged snub during an interview with NBC news on Wednesday, the prime minister said: "I met President Obama last night and we had a long talk about some of the big issues affecting us and I'll be meeting him in Pittsburgh one to one.
"But of course we're meeting all the time. We're both involved in all the main meetings and talk all the time.
"I do say that the special relationship between Britain and America is strong, it continues to strengthen and I think the reason it's strong is that it's based on common values."
He later told the BBC's political editor, Nick Robinson, that he and Mr Obama had "a strong personal friendship".
The prime minister, who earlier referred to his Labour colleagues as "fighters", also said he had been "right" about his actions to restructure Britain's banks and tackle the recession.
Northern Ireland secretary Shaun Woodward told BBC Radio 4's Today programme that the reported snub was the type of "trivia" which tended to accompany prime ministerial trips abroad.
He also said if he counted the times this week the two men had already talked in New York he "would run out of fingers on one hand".
It reveals how keen Labour strategists were to play the Obama and Gordon card before their conference
He was responding to the news that White House officials rejected repeated requests from Britain for a formal meeting - even though the president has held private meetings with the leaders of Japan, China and Russia.
Downing Street said reports of a snub were "completely without foundation".
A spokeswoman said "formal bilaterals were not pinned down", and added: "We have said all along that the meeting situation was fluid, but the prime minister and Barack Obama would be together and have an opportunity to meet which has happened."
Asked whether there were five requests for a bilateral meeting as has been suggested, she said that in the run-up to the trip there would have been numerous calls, but the number was not the issue.
Business Secretary Lord Mandelson dismissed the story of a snub as a "rumour" that ordinary people were not interested in.
"I think it would really just strike them as, frankly, pretty juvenile to have this personality stuff substituted for what really are very serious issues that these leaders are talking about in New York," he told the BBC.
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