(Refiles to add dropped letter in "oil" in headline)
* Hayward hopes cap system will capture most of oil soon
* Says company has financial strength to weather storm
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LONDON, June 6 (Reuters) - BP (BP.L) (BP.N) Chief Executive Tony Hayward told Britain's BBC television a containment cap fitted onto a leaking well in the Gulf of Mexico was capturing a large proportion of the oil and he hoped the vast majority would be under control soon.
Hayward, the subject of speculation that he may be forced out of his position due to the political fallout from the environmental disaster off the southern coast of the United States, said during the interview on Sunday he had strong support from BP's board. "The containment cap is producing around 10,000 barrels of oil a day to the surface which is being processed on the surface," he said.
Asked what proportion that represented of the total oil leaking, Hayward said: "At the moment it's difficult to say but we would expect it to be the majority, probably the vast majority of the oil."
"We are optimising the operation. We have a further containment system to implement in the course of this coming week which will be in place by next weekend. So when these two are in place we would very much hope to be containing the vast majority of the oil," he said.
Public and political pressure has been mounting on London-based BP to cap its gushing seabed oil well and take full financial responsibility for the clean-up and damage caused to Gulf coast fisheries, wildlife and tourism.
Hayward said the company's balance sheet was strong and it was generating a lot of cash flow. It suggests that despite a plunge in the value of its stock it had the financial strength to weather the storm and make a comeback.
"We are going to stop the leak, we are going to clean up the oil, we're going to remediate any environmental damage and we are going to return the Gulf coast to the position it was in prior to this event," he said.
"That is an absolute commitment. We will be there long after the media has gone making good on our promises."
Hayward side-stepped a question on whether the company would go ahead with dividend payments to shareholders. Such a move would be unpopular with many in the United States, who want the company to spend its money on the clean-up and damages claims.
"We are going to take care of all of our stakeholders. We have to care of our Gulf coast stakeholders; we have to take care of our investors; we have to take care of our employees, our retirees," he said.
The CEO said the board would decide at the end of July on whether to pay dividends or not, taking into account all the circumstances.
"BP is running very well today. It's generating a lot of cash. It will to generate $30 to $35 billion of free cash flow this year ... We have the financial strength to see through this," Hayward said. (Reporting by Estelle Shirbon; editing by Karen Foster)