(Updates with BP's letter to the U.S. government, other details throughout) By Susan Daker Of DOW JONES NEWSWIRES HOUSTON (Dow Jones)--BP PLC (BP) could start work on a new effort to contain the oil gushing from the leak in the Gulf of Mexico on Saturday, the federal government's spill-recovery coordinator said Friday. If all goes well, the new system could stop the flow of oil into the Gulf, which has despoiled the Gulf's fragile coast, rendering some fishing areas off limits and soaking untold numbers of sea creatures and birds in toxic crude. To install the device, the cap that's currently in place has to be removed. If this is done before a third collection vessel, the Helix Producer, is brought into full operation, significantly more oil would gush into the Gulf as work on the new containment system progresses. BP and the government have been in talks about the new cap for the past two weeks and on Thursday, Allen sent a letter to the British oil giant demanding it detail its plans within 24 hours. In the company's reply to Allen, released late Friday by the government's spill response team, Chief Managing Director Bob Dudley confirmed that the company has proposed that it start the new containment procedure at the same time that it brings the third collection vessel online, in order to take advantage of an eight-day window of expected good weather. This will leave only one ship, the Q4000, continuing to siphon and burn off oil from the well, cutting the containment rate to about 10,000 barrels a day from around 25,000 until the new system is up and running. Allen said the process of bringing the new containment system online could take several days, but it needs to be started soon because the forecast period of calm weather. The tighter cap will increase the collection system's ability to withstand storms during what's expected to be a very active hurricane season. "We think this weather window presents a significant opportunity for us to accelerate the process of capping--shutting down the well from the top," Allen said. As early as Sunday, BP could start collecting oil with the Helix Producer, which has been near the well site for more than a week, but it hasn't been brought into operation because of bad weather, Allen said. While the new cap could be able to contain all of the oil flowing from the well, BP and the government have always placed more faith in the ability of a relief well to stop the spill. Allen said drilling of the relief well, underway now, could be finished by mid-August. Some BP officials are more optimistic and hope to have it done by the end of July, according to the Wall Street Journal. The spill, the worst offshore leak in U.S. history, that's fouled the coast of at least four states, started in April after Transocean Ltd.'s (RIG) Deepwater Horizon rig blew up and sank about 50 miles off the coast of Louisiana. -By Susan Daker, Dow Jones Newswires; 713-547-9208; [email protected] (Mark Long in New York contributed to this article.) (END) Dow Jones Newswires July 09, 2010 19:19 ET (23:19 GMT)