BP says that the offshore drilling accident that is spewing thousands of barrels of oil a day into the Gulf of Mexico could cost the company several hundred million dollars.

Nobody really knows whether the London-based oil giant is being too conservative about the cost for the April 20 accident, which some experts say could end up as the biggest oil spill in history.

Getty Images A boat works uses a protective boom to collect oil that has leaked from the Deepwater Horizon wellhead in the Gulf of Mexico.

The 1989 grounding of the Exxon Valdez off Alaska, for example, cost Exxon Mobil [XOM 68.75 0.09 (+0.13%) ] more than $4.3 billion, including compensatory payments, cleanup costs, settlements and fines.

But regardless of the out-of-pocket costs, the long-term damage to BP’s [BP 52.2818 -0.2782 (-0.53%) ] reputation — and possibly, its future prospects for drilling in the Gulf of Mexico — is likely to be far higher, according to industry analysts.

The magnitude of the Deepwater Horizon disaster seems to be finally sinking in with investors. BP’s stock plunged more than 8 percent Thursday in American trading in an otherwise strong day for stocks. Since the accident, the American depositary receipts of the company have fallen about 13 percent, closing Thursday at $52.56.

For Tony Hayward, who has led BP for the last three years, the accident threatens to overshadow all of the efforts he has made to burnish the tattered reputation of the company after a refinery explosion in Texas in 2005 and a pipeline leak in Alaska in 2006.

As Mr. Hayward said to fellow executives in his London office recently, “What the hell did we do to deserve this?”

A BP spokesman said no executives were available for an interview Thursday. But in response to a written question, Mr. Hayward said, “Reputationally, and in every other way, we will be judged by the quality, intensity, speed and efficacy of our response.”

So far, the company’s failure to stop the seepage from the underwater well has frustrated government officials. On Thursday, President Obama offered the assistance of an array of government agencies, including the military, while noting that, under federal law, “BP is ultimately responsible for funding the cost of response and cleanup operations.”

Mr. Hayward, who has blamed the rig’s owner and operator, Transocean [RIG 73.35 -5.16 (-6.57%) ], for the accident, said that it was nevertheless BP’s responsibility to deal with the immediate problem. “We take it with the utmost seriousness,” he wrote. “Nothing else matters right now.”

Wall Street experts say that while the company is spending an estimated $6 million a day on fixing the mess, it is impossible to accurately estimate how much the incident will eventually cost.

BP, which leased the platform from Transocean, has said that drilling and operating relief wells to plug the runaway well may cost as much as $300 million, but those same wells will eventually be used to produce profitable oil.

The cost of an environmental cleanup will depend largely on how much oil reaches shore. The government could assess fines or other penalties. And lawyers have already filed a flurry of suits on behalf of commercial fisherman, shrimpers and injured oil workers against BP; Transocean; Cameron, the company that manufactured the blowout preventer; and other companies involved in the drilling process.

Cleanup costs will be divided among BP, which has a 65 percent ownership of the field, and minority partners Anadarko and Mitsui.

Transocean’s stock price fell nearly 7.5 percent Thursday, and is down more than 14 percent since the accident. The company has insurance that covers the rig that was lost, but any broader assessment of Transocean’s liability will be determined after investigators understand what caused the accident.

Regardless of the final assessment of blame, Wall Street analysts warned that everything BP does from now on will come under increased scrutiny by regulators and that potential partners in drilling ventures may well look elsewhere.

“In the last two years, it seemed BP had really cleaned up their act,” said Fadel Gheit, a managing director and oil analyst at Oppenheimer & Company. “Now it looks like a house of cards that has totally collapsed.”

Getty Images Coast Guard Attempts Burning Off Oil Leaking From Sunken Rig

Under Mr. Hayward’s predecessor, John Browne, BP rebranded itself as “Beyond Petroleum,” a company that was environmentally conscious and wanted to develop alternative energy sources like solar and wind power. Its insignia of a blooming flower was intended to portray the company as one that was responsive to growing public concerns about climate change.

But the company seemed to lose its focus on maintenance and safety, BP executives later acknowledged. The 2005 explosion at a refinery in Texas City, Tex., killed 15 workers and injured hundreds more. The Occupational Safety and Health Administration fined BP a record $87 million for neglecting to correct safety violations.

Only a year later, a leaky BP oil pipeline in Alaska forced the shutdown of one of the nation’s biggest oil fields. BP was fined $20 million in criminal penalties after prosecutors said the company had neglected corroding pipelines. Soon after the incident, Mr. Browne quit amid tabloid headlines about his private life.

Mr. Hayward, a geologist who had been in charge of exploration and production, took over and promised to refocus the company and change the culture, emphasizing safety.

He also expanded the company’s already aggressive exploratory efforts in the deep waters of the gulf. Last year, the same platform that has now sunk to the sea floor drilled the deepest well in history, opening one of the largest new fields in the world.

Despite the accident, BP says it remains committed to its gulf drilling program, which contributes 11 percent of the company’s worldwide production.

Senior executives insist that the explosion that sank the Deepwater Horizon rig and killed 11 workers does not reflect the company’s safety standards or Mr. Hayward’s management.

“This accident took place on a rig owned, managed and operated by Transocean,” said Andrew Gowers, a BP spokesman. “It involves the failure of a piece of equipment on that rig. So the unfolding events do not arise from a failure of BP’s safety systems.”

But critics in Congress and elsewhere have questioned BP’s commitment to safety.

Last year, when the federal Minerals Management Service proposed a rule that would have required companies to have their safety and environmental management programs audited once every three years, BP and other companies objected. The agency is also investigating charges by a whistle-blower that the company discarded important records from its Atlantis Gulf platform.

Henry A. Waxman of California, chairman of the House Energy and Commerce Committee, is demanding documents from BP and its drilling contractors in what looks likely to be a full-blown investigation. “A striking feature of the incident is the apparent lack of an adequate plan to contain the spreading environmental damage,” he said in a letter to company officials.

The faltering cleanup effort comes at a time when the company’s business is otherwise going well. Continuing the excellent performance of recent years, BP just announced earnings of $5.6 billion for the first quarter, more than double the profit during the same quarter a year ago.

“Certainly, BP will survive this,” said Cathy Milostan, an oil stock analyst at Morningstar. “This will test Tony and his ability to respond to this situation. We will see if we are seeing a new BP.”