"The people of the Gulf have my commitment that BP will meet its obligations to them," Obama said.
He said the sum of $20bn was by no means a cap. "This is about accountability, at the end of the day that is what every American wants."
Obama also said that the fund would not supersede individuals' or states' rights to present claims in court.
Speaking after the White House meeting, Carl-Henric Svanberg, BP's chairman, said: "We mean what we say, we will look after the people affected."
The spill, he said, was a "tragic accident that should never have happened."
"We have also announced an independent adjudicator that will make sure that the right people will get the right money at the right time."
Tony Hayward, BP's CEO, is expected to continue with the company's apologetic stance when he faces tough questions on Thursdayin the US congress over the crisis.
In prepared testimony obtained by The Associated Press news agency, Hayward expressed contrition for the spill and its effects and said he was "personally devastated" by "these tragic events".
"We will not rest until the well is under control, and we will meet all our obligations to clean up the spill and address its environmental and economic impacts," he is expected to say.
The announcement of the compensation fund is being seen as a much-needed breakthrough for Obama, who has faced growing criticism over his administration's handling of the crisis in the run-up to crucial congressional elections in November.
A recent Associated Press-Gfk poll showed that 52 per cent of Americans were dissatisfied with the government's response to the spill.
Nick Spicer, Al Jazeera's correspondent in Washington, said the ongoing crisis had come to dominate Obama's agenda and was about more than just the oil spill and the compensation.
|BP bosses spent more than four hours in talks at the White House [Reuters]
"It has begun to affect the White House ... politics in general. So it has been pointed out that Obama has to stand up," he said.
The ruptured well has been spewing millions of litres of crude into the Gulf of Mexico since an explosion eight weeks ago destroyed the BP-operated Deepwater Horizon drilling rig, killing 11 workers and setting off an environmental and economic catastrophe.
The spill has so far fouled large swathes of US coastline, damaged multi-billion-dollar fishing and tourism industries, and killed scores of birds, sea turtles and other wildlife.
On Wednesday BP said that it had begun burning off excess oil as well as siphoning off oil spewing from the well.
A containment cap placed on the ruptured well on June 3, has been collecting about 15,000 barrels per day for a week, but it is not stemming all of the oil flow into the Gulf of Mexico.
The cap followed several failed attempted to stop the leak.
BP has said it hopes to install equipment soon to capture as much as 90 per cent of the escaping oil, but the leak is expected to continue at least until relief wells are finished in August.
On Tuesday a team of US scientists significantly revised its estimate of the oil flow rate, increasing it to 35,000-60,000 barrels (5.56 million litres to 9.5 million litres) a day.
|The oil spill has fouled large swathes of US coastline along the Gulf of Mexico [AFP]
The team initially estimated the flow at between 12,000 and 19,000 barrels per day (bpd); last week, it increased that estimate to 20,000 to 40,000 bpd.
All three figures are far above the initial estimate of 5,000 bpd given by BP and US officials at the start of the crisis.
The announcement came on the day Obama, in his first Oval Office address, vowed to make BP pay for the oil spill and outlined a "battle plan" to tackle the destruction caused by the leak.
"We will make BP pay for the damage their company has caused. And we will do whatever's necessary to help the Gulf Coast and its people recover from this tragedy," he said.
Obama said the government would offer additional resources and assistance to the affected coastal states as cleanup efforts continue.
He said that BP would be required to set aside money to pay for the long-term damage.
Obama used the bulk of his speech to renew his pitch for a switch from fossil fuels to clean energy, saying that Americans "must seize the moment" and "accelerate the transition".