Ms Albright said that her conclusion was based on a meeting on Tuesday involving President Bill Clinton and a large group of law-makers.
Speaking to reporters during a photo session with Klaus Kinkel, the German Foreign Minister, Ms Albright said Mr Clinton had not made a decision on the issue. But she said there is a "clear consensus" for carrying out the terms of the Dayton peace accord.
She added that there was agreement also that the Europeans maintain some kind of military or police functions once the Nato mandate expires on 30 June.
The law-makers said, after a two-hour meeting at the White House, that Mr Clinton appeared inclined to extend the US commitment in Bosnia in a yet-to-be defined fashion.
Meeting with about 40 members of the House and Senate late on Tuesday, the President and the Defense Secretary, William Cohen, heard differing views about approaches toward Bosnia. "But with respect to the importance of the US stakes and the stability in the region, there was a general consensus," Ann Luzatto, a White House spokeswoman. said.
While the Republican-led Congress has taken a sceptical view of keeping US troops in Bosnia, a senior Republican senator, John Warner of Virginia, offered strong support for the President.
"It's very clear if the United States pulls out, these unfortunate people will be back at each others' throats again, and we will have lost close to $8bn [pounds 5bn] of US taxpayers' money," Mr Warner said as he left the White House. "I've been coming here 19 years to these meetings and there was not really one voice of any dissent," he said. "It was constructive: `You are the commander in chief, we're going to back you, but here are our ideas'."
Tom Daschle, Senate minority leader, immediately seconded Mr Warner's remarks. "Republicans and Democrats alike have indicated they want to work with the President to construct a strategy that will take us beyond June," he said,
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