NEW ORLEANS, Louisiana — BP has made "significant progress" in installing a new cap over the gushing oil well in the Gulf of Mexico and may be hours away from fitting it in place, officials said Monday.

"We've made significant progress. This could lead to the shutting of the well," Admiral Thad Allen, the former chief of the Coast Guard who is heading the US government's response effort, told NBC television.

In a separate interview on Fox News, Allen said the job was just hours from being finished: "Later on today, the containment cap should be in place."

If engineers succeed in keeping to that timeline, BP could be on the verge of containing the worst environmental disaster in US history, after 13 weeks in which up to half a million barrels of crude has poured into the US Gulf.

"We'll be in a position later today to put the containment cap over the well, and this containment cap will have the ability to actually close down valves and slowly contain all the oil. Once we do that, we'll know how much pressure is in the well," Allen told CNN during his round of morning interviews.

"That could lead to one or two positive outcomes. It could tell us that the well is withholding the pressure and we can shut the well in or just cap it, if you will. Either way, those are two pretty good outcomes," Allen said.

The old cap recovered about 25,000 barrels (over one million gallons) a day, but government estimates put the total flow rate at up to 60,000 barrels a day.

Work is continuing on relief wells to ultimately seal the well.