Oil company BP claimed a significant milestone in efforts to plug a leaking well for good on Wednesday ahead of a U.S. government report that will show most of the spilled crude is already gone.

The world's worst accidental marine oil spill has caused an environmental disaster and shaken the U.S. presidency of Barack Obama. It has also wiped billions of dollars off the value of one of the world's largest oil companies and cost BP's chief executive, Tony Hayward, his job.

But heavy drilling mud pumped into the Gulf of Mexico well on Tuesday to stem the flow of crude is now controlling its pressure, London-based BP said.

The next step in the so-called static kill operation is to pump in cement behind the mud as a seal, but BP said monitoring was required to see whether more mud should be pumped in first.

The MC252 well appears to have reached a static condition -- a significant milestone, it said in a statement

Hayward and his heir apparent, Bob Dudley, are due on Wednesday to visit Russia, home to a quarter of BP's output and a country Dudley fled in 2008 after a dispute with joint venture partners there.

But their minds could be focused on events miles away as efforts to subdue for good the deepwater gusher that was temporarily capped in mid-July reach a climax.

In a preview of a government report on clean-up progress due out later on Wednesday, Obama's main energy adviser appeared to indicate that the scale of the remaining problem might not be as great as some have feared.

The good news is that the vast majority of the oil appears to be gone, Carol Browner said on ABC's Good Morning America.

A New York Times story said the report would show three-quarters of the oil released has already evaporated, dispersed, been captured or eliminated.

The full magnitude of the spill, triggered in April by a deadly rig explosion at the BP-owned Macondo well, became apparent earlier this week as government scientists released revised figures showing almost 5 million barrels of oil leaked before the well was temporarily capped on July 15.

This made it the world's largest accidental maritime release of oil, surpassing the 1979 Ixtoc well blowout in Mexico's Bay of Campeche that gushed almost 3 million barrels.

The spill has disrupted the livelihoods of fishermen and tourism operators and triggered a barrage of damages lawsuits against BP. The company has said it will pay all legitimate claims and clean up fouled beaches and marshes.

INVESTIGATION

Static kill is part of a two-pronged strategy that seeks to finally seal the ruptured Macondo well later in August through a relief well that is still being drilled.

Despite the breakthrough and Browner's comments, the new leak estimates could spell bad news for BP, which also faces an investigation by U.S. securities regulators into whether its employees profited illegally from the spill.

The revised flow numbers suggest the company had underestimated costs by at least $1 billion.

BP had estimated the well had leaked some 4 million barrels of oil and that it would be fined $1,100 per barrel under the Clean Water Act. The company faces fines of $4,300 per barrel if gross negligence is proven, but said it saw no need to change its provision as a result of the new estimate.

BP shares were down 0.25 percent at 1305 GMT on Wednesday at 414.65 pence, slightly outperforming sector rival Shell which was down just over 1 percent. BP stock has recovered about half way from its low point in late June but remains well below its April pre-spill high.

BP has suspended dividend payments, ringfenced $20 billion, and put billions of dollars of its assets up for sale to help pay for its liabilities.

Anadarko Petroleum Corp, one of BP's partners in the well, said on Tuesday it had secured $6.5 billion in loan commitments, in part to pay for its liabilities.

(Additional reporting by Ekaterina Golubkova in Moscow, Rodrigo Campos in New York; Writing by Andrew Callus; Editing by Lin Noueihed)

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