Following a meeting with bosses of the oil giant in the White House, Mr Obama said efforts to contain the leak should capture 90 per cent of the leaking oil in the coming days and weeks.
"That is still not good enough. We will continue to press BP," he added.
BP's chairman, Carl-Henric Svanberg, said yesterday that the company would not pay dividends to its shareholders for the rest of the year.
In a statement, BP said cancelling dividends was "right and prudent".
Previously declared first-quarter dividends, scheduled to be paid on June 21, have been shelved as part of the move.
"The board will consider resumption of dividend payments in 2011," BP said.
Mr Svanberg said: "We regret the cancellation and suspension of the dividends, but we concluded it was in the best interests of the company and its shareholders."
Yesterday's compensation fund and dividend announcement followed a closed-door meeting at the White House at which Mr Svanberg faced a President who has previously displayed his anger over the issue.
During a televised speech to Americans on Tuesday, Mr Obama hit out at BP's "recklessness" over its role in the region's worst environmental disaster.
"BP's liabilities for this spill are significant – they acknowledge that fact," the President said yesterday. But in a conciliatory note, he added: "BP is a strong and viable company and it is in all our interests that it remains so."
Mr Svanberg also acknowledged Mr Obama's frustration.
"He is frustrated because he cares about the little people and we care about the little people," BP's chairman said.
The 20 billion dollar fund will be built up through a series of payments from BP over the next three years.
But it will not serve as a cap on the amount for which BP will be liable – there will be no limit to the compensation account being set up.
Kenneth Feinberg, the lawyer who oversaw compensation payments to the families of victims of the September 11 2001 attacks in the US, will supervise payments.
This will ensure that "the right people will get the right money at the right time", Mr Svanberg said.
Yesterday's White House meeting came a day after the beleaguered firm's debt rating was slashed by a credit agency to near-junk status. Fitch's second downgrade for BP in less than two weeks leaves the blue-chip stock rated at BBB, the agency's lowest investment grade.
The move came on the back of scientists' claims that far more oil was spewing into the Gulf than previously thought and concern over the compensation pot.
Fitch said the company's estimate of clean-up and claims had soared to up to six billion dollars (4.1bn), while fines could be as high as eight billion dollars (5.4bn).
Meanwhile, long-term claims over the spill could drag on for years following the pattern of the Exxon Valdez spill, the ratings agency added.
The cut to BBB will raise the cost of the firm's borrowing as investors demand higher returns for the increased risk.
And a bad week for BP bosses is unlikely to get any better today when chief executive Tony Hayward – who has taken the brunt of the criticism levelled at the firm so far and made a series of press blunders – faces a stormy grilling in Congress.
BP's woes began on April 20 when an explosion sunk its Deepwater Horizon rig, 42 miles off the coast of Louisiana. Eleven workers died in the accident, while more than 100 others needed rescuing. Since then the company's share price has slumped by almost half.