At a news conference, Allen said he has asked BP for a detailed timeline for replacing the existing containment cap with one that will "actually seal the well." He said a third vessel, the Helix Producer, was being connected to the well to suck up the oil that would otherwise go into the Gulf while the caps are being switched.
A 10-day period of good weather in the forecast should allow significant progress, he said.
"We think this weather window presents a significant opportunity for us to accelerate the process of capping -- shutting down the well from the top and increasing the prospects for being able to kill the well from below through the relief wells," Allen added.
The spill began April 20 with an explosion and fire on BP's Deepwater Horizon drilling platform. For weeks, thousands of barrels a day of oil poured unchecked into the Gulf, making the spill the worst in U.S. history.
Celebrity Couples of 2014 [PHOTOS]