SYDNEY, Australia  Australia said Friday that it would not agree to American requests to accept more detainees from the prison at Guantánamo Bay, and Britain signaled reluctance to take in significant numbers of former inmates, underscoring the difficulties both the departing and incoming administrations in Washington face in trying to close the camp, which has stirred bitter controversy around the world.

Australia’s acting prime minister, Julia Gillard, said the Bush administration had twice approached Australia about taking prisoners from the camp, at the American naval base in Cuba.

“The Bush administration first approached Australia in early 2008 with a request to resettle a small group of detainees from Guantánamo in Australia,” Ms. Gillard said Friday in a statement. “After appropriate consideration, Australia declined to allow resettlement of that small group in Australia.”

Early last month, the White House again appealed to Australia and “a number of other friends and allies of the United States,” she said, adding that the request had not come from President-elect Barack Obama. Mr. Obama, who is to be sworn in on Jan. 20, has pledged to close the camp.