25% of BP's total production comes from Russia, largely through the 50-50 joint venture TNK-BP where the International company is partnered with some of the world's richest men.
The company last week announced a 20-billion-dollar compensation fund to deal with claims arising from the spill.
BP is present in Russia through TNK-BP, the third largest oil producer in the country, accounting for roughly a quarter of BP's global production.
Hayward's decision to visit Russia came after Medvedev expressed concern last week over the future of the company, in a newspaper interview.
"What I know is that BP will have to pay a lot of money this year," the president was quoted Thursday as telling the Wall Street Journal.
"Whether the company can digest those expenditures, whether they will lead to the annihilation of the company or its breakup into pieces is a matter of expediency."
As well as being saddled with the huge clean up and compensation costs, the oil firm's credit worthiness has been slashed and its shares have slumped on the stock market in the wake of the spill.
The environmental disaster began on April 20, when a explosion ripped through the Deepwater Horizon rig, killing 11 workers.
Hayward's recent efforts to pacify American anger have proved disastrous, and the oil chief was under fire again Sunday when US politicians blasted him for attending a yacht race.
