NEW ORLEANS ? A rig drilling a relief well meant to stanch a gushing flow of oil into the Gulf of Mexico is ahead of schedule and could reach its target over the next three to four weeks.

That's according to Coast Guard Adm. Thad Allen. He said Thursday that a drill from a rig near the ruptured well is nearly 10,000 feet below the seafloor. He says it should come within 10 feet of the existing well within the next few weeks.

Afterward, the drill bit will bore down about 1,000 feet and then intersect with the damaged well farther underground.

Allen says the final push of drilling is the most difficult. The drilling was originally slated for completion in mid-August.

Once the drill reaches its target, BP will pump heavy mud down the relief well in an attempt to stop the flow.