BP will not make a decision on its next dividend payment until late July, chairman Carl-Henric Svanberg has said.
"The first priority is to do what is right in the Gulf of Mexico," Mr Svanberg said, answering an investor's question on a conference call.
The comment came amid US pressure on BP to cut its dividend to help pay for the Deepwater Horizon oil spill.
He also gave chief executive Tony Hayward the board's full support, after criticism of his handling of the spill.
Before the Deepwater Horizon oil spill began, the company had been expected to pay out $10.5bn (£7.2bn) in dividends over four quarterly payments.
However, two US Senators called earlier this week for the dividends to be cut, so money could be diverted to deal with the Gulf of Mexico oil leak.
Mr Svanberg indicated that, with the ultimate cost of the spill so uncertain, a decision would be made closer to 27 July, when the next dividend payment is due to be declared.
BP's first quarter dividend of $2.6bn has already been declared, and will be paid on 21 June.
BP shares fell at the outset of the call at 1400 BST, before recovering sharply.
Mr Svanberg had appeared to duck the question of dividends in his opening comments, stating merely, "We are aware of the importance of the dividend to you, the shareholders."
Mr Hayward also avoided any explicit commitment to maintain the company's dividend on the call.
"We will stand behind all of our commitments," he said, before going on to note the need to balance paying dividends with other demands on the company.
"We will meet the obligations to our employees and other stakeholders, including hundreds of thousands of shareholders," the BP head said.
Mr Hayward said the company had already spent more than $1bn (£686m) on dealing with the spill, and expected to continue spending at this rate until some time after the leak is stopped.
"It is simply not possible to put a cost estimate on this at the moment," he said.
He added that by the time BP releases its second quarter results, due in July, they hoped to have a better idea of the ultimate cost.
However, he emphasised that some costs, including fines, remediation costs and lawsuits, would go on for many years.
Mr Hayward also said it would be another two days before BP knew whether it had plugged the Deepwater Horizon oil spill.
"It will be a further 48 hours before the system can be optimised," he said, adding that only then would they know how much of the oil and gas from the leak was being captured.
He said "everyone at BP is heartbroken" by the loss of life and economic and ecological damage from the spill, and offered his personal apology.