The US president said if any laws were broken, people will be prosecuted.
Mr Obama spoke in the White House's Rose Garden after meeting the co-chairmen of the commission, Bob Graham, a former Florida governor and US senator, and William Reilly, a former head of the Environmental Protection Agency.
"They have my full support to follow the facts wherever they lead, without fear or favour," he said.
The president said that if laws were insufficient, they would be changed. He said that if government oversight was not tough enough, that will change, too. And Mr Obama said if laws were broken, those responsible will be brought to justice.
Mr Obama directed the co-chairmen to report back in six months "with options for how we can prevent and mitigate the impact of any future spills that result from offshore drilling".
Attorney General Eric Holder also planned to visit the Gulf coast to see areas affected by the oil spill and to meet state attorneys-general and US prosecutors.
Several senators have asked the justice department to determine whether criminal or civil laws were broken in the spill. The justice department has told Senator Barbara Boxer, who heads the Senate's environment committee, that it has ordered BP not to destroy documents that could be relevant in an investigation.
The independent commission's inquiry will range from the causes of the spill to the safety of offshore oil drilling and the functioning of government agencies that oversee drilling.
Amid concern that the worst oil spill in US history could threaten his presidency, President Obama has stepped up his public appearances to demonstrate that he is engaged with the problem.
In the six weeks since the rig exploded, the US government estimates that between 75 million litres and 163 million litres of crude oil have poured into the Gulf – affecting beaches, wildlife and the local economy and making it the worst spill in US history.
Yesterday the US secretary of homeland security Janet Napolitano said BP should be planning now to pay the immense costs of containing and cleaning up the oil spill.
"Our intent is that BP will pay the entire bill," she said. "How that is done, what assets they need to deploy in order to do that, I think again it is premature to say.
"They have lots of assets and should be reserving now and planning now to pay for the immense costs of these containment and clean-up efforts," she said.