WASHINGTON (Reuters) - Under intense pressure from President Barack Obama, BP Plc agreed on Wednesday to set up a $20 billion fund for damage claims from its huge Gulf of Mexico oil spill and suspended dividend payments to its shareholders.

The deal gave Obama his most tangible success since the crisis began 58 days ago and came after weeks of criticism of his handling of the disaster. It also eased U.S. pressure on BP, whose share price has withered amid uncertainty over the spill’s cost to the British energy giant.

Obama announced the agreement after White House officials held four hours of talks with BP executives, who emerged to offer an apology to the American people for the worst oil spill in U.S. history.

“I do thank you for the patience that you have during this difficult time,” BP Chairman Carl-Henric Svanberg said. “I hear comments sometimes that large oil companies are greedy companies who don’t care. But that is not the case in BP. We care about the small people.”

Svanberg promised to make sure damage claims are handled swiftly and fairly.

Chief Executive Tony Hayward, the public face of BP’s response to the disaster, will appear on Thursday at a congressional hearing where he will face intense scrutiny over events leading up to the spill and BP’s cleanup of the mess.

An April 20 explosion on an offshore rig leased by BP killed 11 workers and ruptured a deep-sea well. The ensuing spill has fouled 120 miles of U.S. coastline, imperiled multibillion-dollar fishing and tourism industries and killed birds, sea turtles and dolphins.

“THEY’LL NEED MORE”

While Obama stressed the agreement would not cap BP’s total liabilities, Wall Street appeared to cheer the small dose of clarity the deal provided, driving up the company’s share price by 1.5 percent in New York.

Under the agreement, BP committed to pay $20 billion into an independently managed fund over four years, suspend dividend payments for the rest of the year and pay $100 million to workers idled by the six-month moratorium on deep-sea drilling that the Obama administration imposed after the spill.

The $20 billion figure is roughly equal to BP’s average annual profits over the past four years. BP is expected to report net profits of $18.9 billion in 2010, according to Thomson Reuters I/B/E/S consensus estimates.

“We will continue to hold BP and all other responsible parties accountable,” Obama said at the White House. “And I’m absolutely confident BP will be able to meet its obligations to the Gulf Coast and to the American people.”

The fund will be administered by Kenneth Feinberg, the Obama administration official who oversaw compensation for executives at companies that received federal bailout funds.

Obama had pressed BP to set up a fund administered by a third party after hearing first-hand complaints from Gulf Coast residents that BP’s claims process was too complicated and the company was paying out too little money.

With thousands of Gulf Coast commercial fishermen largely idled by the spill, Louisiana shrimper Clifton Bartholomew, 21, wondered whether $20 billion would be enough.

“If you add it all up together -- everybody in shrimping, fishing, the whole industry -- by the time this is all gone I think they’ll need more than $20 billion,” Bartholomew said.

BP said in a statement it would cut three quarters of dividends, significantly reduce its investment program and sell $10 billion of assets to create the fund.

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The commitments are harsher penalties than most investors had hoped for. They had not expected BP to be forced to sell assets and cut investment -- moves that would curb its growth.

BP said it would cancel the first-quarter dividend due for payment on June 21 and would not declare interim dividends for the second and third quarters of 2010. The payouts were expected to be about $2.6 billion per quarter, in line with recent quarters.

“STRONG AND VIABLE COMPANY”

Obama stressed BP was “a strong and viable company, and it is in all of our interests that it remain so.”

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The oil giant represents a large part of investment portfolios in Britain. Obama and British Prime Minister David Cameron talked about the issues around the spill last weekend.

BP’s shares gyrated in volatile New York trading, dropping as much as 5 percent before swinging to positive territory on news of the agreement on the fund, known as an escrow account.

“It’s a step in the right direction for BP but unfortunately I cannot say the same for Tony Hayward because it is going to get tougher for him,” said Fadel Gheit, managing director of oil and gas research at investment firm Oppenheimer & Co in New York

“Tomorrow he’s going to be in the hot seat under glaring lights and tremendous animosity and criticism” at the hearing.

The BP chief executive will tell lawmakers the entire oil and natural gas industry needs to be better prepared for deepwater accidents, according to his prepared testimony.

That is an apparent response to attempts by rival oil companies to distance themselves from BP’s disaster at a hearing on Tuesday.

As BP stock saw some relief, shares in Anadarko fell 3.69 percent and Transocean lost 3.09 percent in New York. Anadarko is part owner of the blown-out well and Transocean owned the rig that blew up.

Back in the Gulf, BP said it started a second system to siphon oil from the leak on Wednesday, a day after a team of U.S. scientists raised their high-end estimate of the amount of crude oil flowing from the well by 50 percent to between 35,000 and 60,000 barrels per day.