Engineers have stopped the flow of oil and gas into the Gulf of Mexico from a gushing BP well, the federal government’s top oil spill commander, U.S. Coast Guard Adm. Thad Allen, said Thursday morning.

The “top kill” effort, launched Wednesday afternoon by industry and government engineers, has pumped enough drilling fluid to block all oil and gas from the well, Allen said. The pressure from the well is very low, but persists, he said.

[For the record, 6:39 a.m.: An earlier version of this story termed the effort “successful.” Officials clarified that neither government nor BP officials had declared the effort a success yet. They caution that only after the cementing is complete and the well is sealed can the top kill be called successful.]

Once engineers have reduced the well pressure to zero, they will begin to pump cement into the hole to entomb the well. To help that effort, he said, engineers are also pumping some debris into the blowout preventer at the top of the well.

Allen said one ship that was pumping fluid into the well has run out of the fluid, or “mud,” and that a second ship is on the way. He said he was encouraged by the progress.

“We’ll get this under control,” he said.

Allen also said that later today, an interagency team will release a revised estimate of how much oil was flowing from the well into the Gulf before the “top kill” effort began. The Coast Guard has estimated the flow at 5,000 barrels a day, but independent estimates suggest that it was much higher ÃÂ perhaps tens of thousands of barrels a day.

jim.tankersley@latimes.com