Early Saturday, engineers were able to divert only 6,000 barrels in a 24-hour period to a ship on the surface as they worked to close two of four vents on the containment cap. But by midnight, according to Admiral Allen, the amount of oil diverted to the ship had reached 10,000 barrels.

Image Workers removed small globs of oil that had washed up on Pensacola Beach in Florida. Credit... Joe Raedle/Getty Images

Admiral Allen’s estimate of the effect of the new cap was echoed by Tony Hayward, the chief executive of BP, in a BBC interview broadcast Sunday, who also said that another containment system would be put in place by next weekend. “So when those two are in place, we would very much hope to be containing the vast majority of the oil,” Mr. Hayward said.

Admiral Allen said that engineers hope to gradually increase the amount of oil captured into a nearby ship without jeopardizing the delicate recovery effort after so many other efforts failed in the last six weeks. The disaster began after the Deepwater Horizon drill rig exploded on April 20, killing 11 workers.

Oil was still escaping through four vents on the top of the cap that are designed to relieve pressure and not overstress the containment system. Admiral Allen said that if the vents were closed too quickly, cold sea water could rush in and form the kind of icy hydrates that doomed a previous attempt to cap the spill.

The admiral had initially said that they hoped to begin closing the vents on Friday. But on Saturday he said that they had been unable to do so because the pressure inside the containment cap might become so great that oil would blast through the imperfect seal connecting it to the riser pipe.