Washington (CNN) -- Drilling of two "relief wells" -- viewed as the ultimate solution to the Deepwater Horizon gusher -- continue to be ahead of schedule, and the first well could reach its goal in three or four weeks, several weeks ahead of the projected mid-August date, Coast Guard Admiral Thad Allen said Thursday.
But he shied away from saying the well would be plugged early, citing the complexity of the operation.
"They're actually ahead of schedule right now, but I'm not going to guarantee it will be early," said Allen, the federal officer overseeing the spill response. "As I said earlier, we should be very wary about deadlines."
One drilling rig is at 9,967 feet below the sea floor and is "starting to close in on the well bore itself," Allen said, while a back-up rig is at 4,560 feet below the sea floor.
The relief wells are expected to tap into the existing Deepwater Horizon well bore about 13,000 feet below the sea floor, according to BP's on-line schematic of the relief well plan. That is a few hundred feet above where the pipe enters the oil reservoir.
"We anticipate over the next three to four weeks, they will close in and be able to tap into the well (bore) itself," he said. "At that point they will pump mud down it in an attempt to do what we call the bottom kill and actually cap the well."
At that point, the drilling will tap into the Deepwater Horizon pipe and pump heavy fluid or "mud" into the pipe. Since the mud is denser than oil, it should stem the flow of the oil. Cement will then be pumped down to permanently seal the well.
Pressed on whether the well could be plugged earlier than previously forecast, Allen urged caution, saying the "directional drilling" needed to hit Deepwater Horizon's 7-inch well bore needed to be "very exact." Allen said his is not prepared to predict anything beyond the mid-August date.
This isn't the first time authorities have said the relief well drilling was ahead of schedule. At the end of May, the government reported the first relief well was 10 days ahead of schedule.