BP will begin replacing the cap on its runaway well in the Gulf of Mexico with a new one that has a tighter seal and could funnel all the oil spewing from the well to surface ships, the leader of the federal response effort said Friday.

The leader, Thad Allen, a retired Coast Guard admiral, said at a briefing in New Orleans that, perhaps as early as today, technicians would remove the containment cap at the top of the failed blowout preventer, the giant stack of safety devices on the seabed. It will then take three to four days to install the tighter cap, during which time oil will gush unabated from the top of the well, he said.

If all goes as planned, the new cap could effectively contain the leaking well by sometime next week. But like other engineering efforts in the 11 weeks since oil began pouring into the gulf after the Deepwater Horizon rig explosion, there is no guarantee that technicians, using remotely operated submersibles 5,000 feet underwater, will succeed in installing the cap. If the procedure fails, the old cap would have to be reinstalled.

That cap is now diverting about 15,000 barrels of oil a day to a surface ship, the Discoverer Enterprise. This amount “will have to be released while we’re putting the new cap on,” Allen said. The work should not affect a second system that is collecting 8,000 to 9,000 barrels a day from a pipe lower on the blowout preventer.

Allen said that after consulting with officials from BP and the National Oceanic and Atmospheric Administration, he had directed BP to provide a timeline to “accelerate the replacement of the current containment cap,” to take advantage of a spell of good weather expected to last seven to 10 days.

In a letter Friday responding to Allen’s request for a timeline, BP’s chief managing director, Robert Dudley, said the company had originally planned to install the tighter cap after a third system involving another surface ship, the Helix Producer, was up and running. But because of the weather window, he wrote, BP, “in conjunction with government experts,” had proposed that the new cap “be implemented in parallel with the startup of the Helix Producer.”