The US Attorney General, Eric Holder, on a visit to Louisiana coast, said an investigation had been opened and that federal agencies, including the FBI, were participating. "If we find evidence of illegal behavior, we will be forceful in our response," Mr Holder said.

As BP shares plunged 13pc in London, Tony Hayward, the company's chief executive, admitted he is facing a difficult fight on the home front as well.

Investors are abandoning the oil giant as concerns grow about its ability to fund the clean-up operation, compensation claims and extra safety rules. Experts estimate the final cost, stretching over a number of years, could top $30bn (£20bn).

Mr Hayward says worries about BP's balance sheet are "completely unfounded", despite the £40bn fall in its market value since the disaster a month ago.

"There's a big buffer," he insisted in an interview with The Daily Telegraph. "The worry about the dividend is overstated."

Despite BP's continued failure to plug the leaking Macondo well, Mr Hayward and colleagues will divert their attentions from the operation to address shareholders this week.

The move underlines how seriously BP is taking the 34pc drop in its share price, which analysts believe could leave it vulnerable to short-sellers or even make a takeover target. "We need to go out to them and engage," the BP boss said. "We will listen to what they have to say."

The balance sheet is not the only concern. Many are also worried that Mr Hayward has failed to charm America, saying tactlessly on Tuesday that he would "like [his] life back" and at first insisting that the spill's impact was "very, very modest".

Meanwhile, BP's all but invisible chairman, Carl-Henric Svanberg, has not been on the front line supporting his chief executive as the company faces unprecedented pressure to explain its conduct and, in the words of President Obama, "plug the damn hole". At such a stressful time, Mr Hayward believes it is easy to forget that the rest of the company is functioning successfully and this is the message he will be taking to shareholders.

"It's important to remember the company is working very well operationally," Mr Hayward said. "We've had a record quarter one results; ahead of expectations, strong cash flow and operating performance. None of that has changed. Our cash flow is sufficient to invest for the future, pay the dividend and have $6bn-$8bn surplus cash flow after that."

For the first time, he gives an estimate of the worst-case scenario costs for BP in terms of paying for the clean-up and efforts to plug the well. The operation has cost $1bn so far, and another $2bn-$3bn could be added if the well is still not plugged until the end of August.

Even with extra clean-up and compensation costs, Mr Hayward believes that "relative to the company's cash flow it's manageable".

He is also likely to want to allay investor concerns about the political risk of owning shares in the company, as rhetoric against BP grows ever more aggressive.

Last week, Russia expressed doubts about BP's environmental record and its future as an energy major extracting a quarter of its oil and gas from the notoriously difficult country.

Mr Hayward admitted that BP needs to be "on its guard" about any hostility. Russia, after all, is known for seizing energy assets from foreign companies. "But we haven't seen anything untoward at the moment," he added.

Another 25pc of BP's production capacity is in the US, with its most promising prospects in the Gulf of Mexico. As for any assets seizures by President Obama's sabre-rattling administration, Mr Hayward describes that as "highly unlikely". "There are other forms of redress that are far more conventional," he said.

The price of BP's continued presence in the US is more likely to be hand-wringing, improved safety and compensation – and although Mr Hayward denies it – maybe that old City sacrifice, the boss's head.

www.telegraph.co.uk/finance/newsbysector/energy/oilandgas/7795014/Gulf-of-Mexico-oil-spill-BP-and-Hayward-fight-for-their-survival.html