Growing confidence in the experimental cap's security convinced scientists it was safe to leave it unmonitored for a few days, Retired Coast Guard Adm. Thad Allen said.
Allen said they'll decide Thursday evening whether ships will have to leave.
"The decision has been made to leave the cap on, even if the well is unattended," Allen said.
Forecasters at the U.S. National Hurricane Center in Miami say the storm system has already caused flooding in Puerto Rico, the Dominican Republic and Haiti. It could become Tropical Storm Bonnie later Thursday and reach the Gulf of Mexico by Saturday.
Seas already were choppy in the Gulf, with waves up to five feet rocking boats as crews prepared to leave if needed. Some boats involved in the cleanup were called into port Thursday, Coast Guard Rear Adm. Paul Zukunft said. He also directed workers to remove oil-absorbent booms from marsh areas along the coast to prevent damage to ecologically sensitive areas. Work on plugging the well is at a standstill just days before the expected completion of a relief tunnel to permanently throttle the free-flowing crude.
Crews had planned to spend Wednesday and Thursday reinforcing with cement the last few feet of the relief tunnel that will be used to pump mud into the gusher and kill it once and for all. But BP put the task on hold and instead placed a temporary plug called a storm packer deep inside the tunnel, in case it has to be abandoned until the storm passes.
"What we didn't want to do is be in the middle of an operation and potentially put the relief well at some risk," BP vice president Kent Wells said.
If the work crews are evacuated, it could be two weeks before they can resume the effort to kill the well. That would upset BP's timetable, which called for finishing the relief tunnel by the end of July and plugging the blown-out well by early August.
As the storm drew closer, boat captains hired by BP for skimming duty were sent home and told they wouldn't be going back out for five or six days, said Tom Ard, president of the Orange Beach Fishing Association in Alabama.
Even if the storm does not hit the area directly, it could affect the effort to contain the oil and clean it up. Hurricane Alex stayed 500 miles away last month, yet skimming in Alabama, Mississippi and Florida was curtailed for nearly a week.
The relief tunnel extends about two miles under the seabed. It's now about four feet from the side of the well, although BP still has more than 100 feet to drill diagonally before the tunnel reaches the well. BP plans to insert a final string of casing, or drilling pipe, cement it into place, and give it up to a week to set, before attempting to punch through to the blown-out well and kill it.
BP's broken well spewed somewhere between 94 million and 184 million gallons into the Gulf before the cap was attached. The crisis -- the biggest offshore oil spill in U.S. history -- unfolded after the BP-leased Deepwater Horizon rig exploded April 20, killing 11 workers.
The cause of the blast is still under investigation, but there have been repeated questions raised by rig workers over the equipment and safety conditions aboard the rig.
The New York Times reported early Thursday that rig workers said in a confidential survey before the April 20 explosion that they were concerned about safety and the condition of some equipment on board.
The Times reported that another report conducted for Transocean by Lloyd's Register Group found that several pieces of equipment -- including the rams in the failed blowout preventer on the well head -- had not been inspected since 2000, despite guidelines calling for inspection every three to five years. Transocean said most of the equipment was minor and the blowout preventer was inspected by manufacturer guidelines.
A spokesman for Transocean, the owner of the rig leased by BP, confirmed the existence of the reports to The Associated Press.
"As part of Transocean's unwavering commitment to safety and rigorous maintenance discipline on all our rigs, we proactively commissioned the safety survey and the rig assessment review," Transocean spokesman Lou Colasuonno said in an e-mail early Thursday. "A fair reading of those detailed third-party reviews indicates clearly that while certain areas could be enhanced, overall rig maintenance met or exceeded regulatory and industry standards and the Deepwater Horizon's safety management was strong and a culture of safety was robust on board the rig."