The two leaders met in July, during the presidential election campaign
White House officials rejected repeated requests from Britain for a formal meeting between President Barack Obama and Gordon Brown, it has emerged.
The prime minister's team were "frantic" after being unable to secure the talks at the UN summit in New York, a diplomatic source has told the BBC.
However, the president held private meetings with the leaders of Japan, China and Russia.
Downing Street said reports of a snub were "completely without foundation".
A spokesman said the men had had a "wide-ranging discussion following last night's climate change dinner".
It has emerged this was a few minutes of conversation in a kitchen at the United Nations.
Any stories that suggest trouble in the bilateral relationship between the United States and UK are totally absurd
The spokesman went on to say the prime minister and president would co-chair an "important" meeting on Thursday on Pakistan, and would have further meetings at the G20 later this week.
The BBC's political editor Nick Robinson said Mr Brown wanted a similar event to the substantial meetings President Obama held with the leaders of Japan, China and Russia.
But the White House rejected that Mr Brown had been given a lower priority than other leaders.
A spokesman said: "Any stories that suggest trouble in the bilateral relationship between the United States and UK are totally absurd.
"We would add that President Obama and Prime Minister Brown enjoy a terrific relationship, they speak regularly on a range of the most difficult challenges facing our two nations and meet frequently."
The spokesman pointed to "the tight and extensive work our countries carry out together to address common challenges across the globe" as evidence of the closeness of the relationship.
The row comes after Mr Obama described the Lockerbie bomber's release as a "mistake".