A new containment cap that BP plans to place over the leaking oil well in the Gulf of Mexico has the potential to halt the flow of crude oil in mid-July, a BP executive said Monday.

In a technical briefing for reporters, BP Senior Vice President Kent Wells said that replacement of the oil containment cap with a bigger cap, which could happen as soon as two weeks, could stop the oil leak under the right circumstances.

“A lot depends on the pressure response we see,” he said. “… If the capability is there to stop the flow, we’ll do that.”

If successful, the new capping operation would cut several weeks off BP’s previous estimate of when it would be able to shut off the leak by drilling a relief well.

West said that the relief well operation is continuing to make good progress and has come within 20 feet of the Macando well that has been spewing oil into the Gulf since April 20. From here, engineers plan to drill another 900 feet or so vertically, paralleling the runaway well and conducting “ranging” tests to ensure they are locked onto the target.

“By running parallel … we are going to know exactly where that well is,” he said. “… Having the ability to do that really increases the probability of success.”

Despite the progress, West declined to move up the timetable for completion of the relief well, which is still expected in early August.

Here’s an informative BP video explaining how the relief well operation is supposed to work.