The president's remarks came after he met Bob Graham, a former senator, and William Reilly, a former Environmental Protection Agency administrator, who are co-leading a presidential commission into the oil spill.
Obama pledged that the 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.
Holder, making his first visit to the disaster site where he took a tour of the spill, said he saw "oil for miles and miles, oil that we know has already affected plant and animal life along the coast".
"We have begun both a criminal as well as a civil investigation as is our obligation under the law," Holder told reporters after meeting with state and federal prosecutors in New Orleans.
Federal agencies, including the FBI, are participating in the probe and "if we find evidence of illegal behaviour, we will be forceful in our response," he said, adding that prosecutors had "sufficient basis" to start a criminal probe.
Holder declined to say who were the targets of the investigation, but the justice department has already demanded that at least three companies involved in the spill, BP, Transocean Ltd and Halliburton, preserve their records related to the accident.
Pressure has been building on oil giant BP and the Obama administration to stop the gushing oil, now in its 43rd day and with no end in sight.
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 the drilling of relief wells is expected to be completed.
With the ambitious "top kill" attempt having failed to stop the massive leak over the weekend, BP was scrambling to start yet another attempt to solve the problem.
An effort to saw through the pipe leaking the oil and cap it, could be tried as soon as Wednesday.
But the risky procedure, in which the company will put a lid on the spewing wellhead so oil can be siphoned to the surface, could, at least temporarily, increase the oil flow.
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 passes through the area.
The Atlantic hurricane season started on Tuesday, raising fears that the oil crisis could get a lot worse.