Obama commented after BP officials reached the disappointing conclusion that a dayslong effort to stop the flow of oil, known as a "top kill," by packing the well with mud had failed.
It was the latest in a series of failed attempts by BP to cut off the flow of oil.
BP will now try anew by cutting the pipe that lies deep underwater and fitting a containment valve over the leak, an effort expected to take four to seven days.
The disappointing news came a day after Obama interrupted a long holiday weekend at his home in Chicago to visit the Louisiana coast on Friday and show its angry residents that he is in command of the situation.
"As I said yesterday, every day that this leak continues is an assault on the people of the Gulf Coast region, their livelihoods, and the natural bounty that belongs to all of us," Obama said. "It is as enraging as it is heartbreaking, and we will not relent until this leak is contained, until the waters and shores are cleaned up, and until the people unjustly victimized by this manmade disaster are made whole."
Obama said he discussed the situation Saturday with Coast Guard Adm. Thad Allen, who is overseeing the response to the spill, and Energy Secretary Steven Chu, Interior Secretary Ken Salazar, Environmental Protection Agency Administrator Lisa Jackson, and senior White House advisers John Brennan and Carol Browner.
Obama said the approach BP plans to turn to next is risky and hasn't been tried before at a depth of 5,000 feet.
He said that while officials were hopeful the "top kill" procedure would succeed, "we were also mindful that there was a significant chance it would not."
Obama pledged anew to pursue "any and all responsible means" of stopping the leak until BP completes the drilling of a relief well. But while the relief well is permanent solution to the problem, BP says it won't be ready until August.
In the six weeks since the spill began, the government estimates that between 18 million and 40 million gallons of crude have poured into the Gulf, damaging beaches and wildlife and the local economy.