The president delivered the threat after meeting Bob Graham, a former senator, and William Reilly, a former Environmental Protection Agency administrator, who will co-chair a presidential commission into the oil spill.
Obama said that the presidential commission, which will have six months to make a report, will offer victims of the oil spill and future generations, a "full and vigorous" accounting of what happened.
Meanwhile, shares in BP dropped sharply as markets reacted to the failure of the energy giant's latest effort to contain the oil spill in the Gulf of Mexico.
The company's shares closed down 13 per cent in trading in London, wiping $17.4bn off BP's market value after weekend news that its latest attempt to plug its blown-out seabed had failed.
The shares have lost more than a third of their value, or $67bn, since the leak started six weeks ago.
The cost of dealing with the environmental crisis now totals $990m and there are fears the spillage of oil will now go on until at least August, when relief wells have been drilled.
With the ambitious "top kill" attempt having failed to stop the massive leak over the weekend, BP is ramping up its efforts to solve the problem.
Another temporary fix, an effort to saw through the pipe leaking the oil and cap it, could be tried as soon as Wednesday.
The risky procedure, in which the company will put a lid on the leaking wellhead so oil can be siphoned to the surface, could, at least temporarily, actually increase the oil flowing from the busted well.
Using robot submarines, BP plans to cut away the riser pipe this week and place the cap-like containment valve over the blowout preventer.
On Monday, live video feeds showed robot submarines moving equipment around and using a circular saw-like device to cut small pipes at the bottom of the Gulf.
"We are well into the operation to put this cap on the well now," Bob Dudley, BP's managing director, told NBC, a US television channel, on Tuesday.
BP failed to plug the leak on Saturday with its top kill procedure, which shot mud and pieces of rubber into the well but couldn't beat back the pressure of the oil.
The company also wants to build a new freestanding riser to carry oil toward the surface, which would give it more flexibility to disconnect and then reconnect containment pipes if a hurricane passed through.
Neither of those plans would start before mid-June and would supplement the cut-and-cap effort.
But the best chances for sealing off the leak are two relief wells, the first of which won't be ready until August.
The spill has already leaked between 19.7 million and 43 million gallons, according to government estimates.
Tuesday is the official start of the 2010 Atlantic hurricane season, which forecasters say may be the most intense since 2005.
That year Hurricane Katrina ravaged the region and disrupted offshore oil and gas output.
Experts fear a big storm could drive more oil ashore and force BP and the US government to suspend cleanup efforts.
More than 200km of Louisiana's coastline has already been hit with oil, including the resort of Grand Isle near Port Fourchon.