HOUSTON—BP P.L.C. was working Friday to remove the failed blowout preventer from the Deepwater Horizon oil rig that leaked millions of barrels of oil into the Gulf of Mexico.

Meanwhile, the Gulf Coast Claims Facility established by BP and run by a neutral administrator is paying more than twice the amount per claim than the oil giant was paying on its own, BP said.

In an update on its website, BP said it began removing the failed blowout preventer Thursday and would replace it with a new blowout preventer.

Drilling of the relief well, which BP estimated likely would intercept the Macondo oil well in mid-September, has stopped until the blowout preventer is replaced.

No new oil has flowed into the Gulf of Mexico from the well on which the Deepwater Horizon was working since July 15, when the well was shut in, BP said.

The leak began when the Deepwater Horizon caught fire April 20, killing 11 workers on the oil rig, which sank two days later and caused the spill.

BP said the last controlled burn of surface oil was on July 20, and “no volumes” of oily liquid had been recovered since then. The company said skimming operations recovered 826,000 barrels of oily liquid and controlled burns removed an estimated 265,000 barrels of oil.

Meanwhile, all claims by individuals or businesses affected by the spill were transferred Aug. 23 to the Gulf Coast Claims Facility, a neutral entity administered by Kenneth R. Feinberg.

So far, the facility has paid out $38.5 million on 4,900 claims, nearly $7,900 per claim, BP said. BP said it already had paid $399 million on 127,000 claims, or about $3,100 per claim.