Almost three-quarters of the oil spilled in the Gulf of Mexico has been cleaned up or broken down by natural forces, the US government says.
White House energy adviser Carol Browner said only a quarter of the leaked oil posed any further danger to the environment.
The majority had been captured, burned off or evaporated, she said.
She was speaking after BP announced its "static kill" procedure was working. Barack Obama welcomed the news.
"So, the long battle to stop the leak and contain the oil is finally close to coming to an end. And we are very pleased with that.
"Our recovery efforts, though, will continue. We have to reverse the damage that's been done," he said.
A 'big step'Speaking on the ABC television network, Ms Browner said: "The scientists are telling us about 25% was not captured or evaporated or taken care of by mother nature."
She said the inter-agency report was "encouraging", but added that more cleanup was necessary.
"This is an initial assessment by our scientists in the government and outside the government. We think it's important to make this available to the public. That's what we'll be doing today," she said.
The New York Times said the report from the National Oceanic and Atmosphere Administration indicated it was unlikely beaches along the Gulf of Mexico would be covered by surfacing oil in the future.
And although the report may claim residents along the Gulf will not see their beaches coated with oil, Ms Browner warns we may continue to see effects from the disaster.
"Mother nature will continue to break it down. But some of it may come onshore, as weathered tar balls. And those will be cleaned up. They can be cleaned up. And we will make sure they are cleaned up," she said.
Meanwhile, BP says the "static kill" of its ruptured Gulf of Mexico oil well has worked, a big step towards sealing it.
On Tuesday, the oil giant began pumping a drilling fluid known as mud into the well from vessels on the surface.
Experts believe the mud will force the oil back down.
Workers stopped their static kill procedure after eight hours to monitor the well and make sure it remained stable.
BP said well pressure was being controlled by the pressure of the mud, which was "the desired outcome".
A 18,000ft (5486m) relief well is also currently being drilled, which BP will use later this month to perform a "bottom kill" procedure.
Retired Coast Guard Adm Thad Allen said mud and cement would be injected into the bottom of the damaged well as the last step in the process to permanently stop the leaking oil.
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"There should be no ambiguity about that. I'm the national incident commander, and this is how this will be handled," Adm Allen said
Efforts to kill the well are becoming increasingly important as hurricane season approaches in the Gulf.
Oil began flowing into the Gulf after an explosion on the Deepwater Horizon drilling rig in April. Eleven workers were killed in the blast.
The leaking oil was stopped on 15 July when BP closed a new cap it placed on the leaking well.
An estimated 4.9 million barrels of oil leaked into the waters of the Gulf during 87 days, with only 800,000 barrels being captured.
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