Russia's top energy official said he expected BP chief executive Tony Hayward to step down soon, ahead of a meeting with him in Moscow later today.

"We know that Tony Hayward is leaving his position and he will introduce his successor," Igor Sechin told reporters ahead of his meeting with the embattled BP boss. Sechin, Russia's deputy prime minister and the chairman of the country's biggest oil company Rosneft, was responding to a question about what would be discussed at the meeting.

BP denied that Hayward was close to resigning. "Tony Hayward remains the chief executive of BP. There are no plans for him to resign," a spokeswoman said.

Sechin is a close ally of Russia's prime minister Vladimir Putin, and the leader – at least unofficially – of the Kremlin's hardline siloviki faction made up of former KGB officers. A one-time Soviet military intelligence agent, Sechin presides over an impeccable network of sources, both formal and clandestine, all across the oil industry. His comments about Tony Hayward's imminent departure from BP are unlikely to have been made by accident.

The reports further boosted BP's shares, already up this morning on hopes that the oil giant will be able to plug the oil leak in the Gulf of Mexico earlier than thought, to 311.9p, a gain of 7.3p or 2.4%. On Friday the shares crashed to a 14-year low of 304p, down over 6%. More than £60bn has been wiped off the company's market value since the rig explosion on 20 April.

Hayward's visit to Moscow is the first since the oil spill, and comes amid Kremlin worries over BP's future. Its Russian venture TNK-BP is responsible for a quarter of BP's global oil output. The Russian ambassador to Britain has said his government wants guarantees from BP that the venture would not be affected by its growing bill for the oil spill.

BP said this morning it was now spending $100m (£66m) a day on efforts to contain and clean up the massive oil spill in the Gulf of Mexico, bringing its total bill to $2.65bn so far.

The oil giant spent $300m on containing the oil spill in the past three days. Its total bill is up from Friday's figure of $2.35bn. That includes the cost of trying to cap the well, clean up the environmental damage caused by the leak and pay compensation to those affected. BP has paid out more than $128m to fishermen and others.

BP said today it remained on track to complete its relief well, which is designed to kill the leaking well, within the three months envisaged in May. But according to reports, the company is now hoping to seal the well by mid-July, rather than early August.

There was more good news as the US National Hurricane Centre in Miami said that tropical storm Alex, which has pounded parts of Central America and is heading towards Mexico's Caribbean coast, was likely to strike well away from the area where BP is trying to stop the oil leak.

Barack Obama and David Cameron said that the oil giant should "remain a strong and stable company" after meeting to discuss the environmental disaster on the sidelines of the G20 summit in Toronto.