BP Plc and Russia's state-controlled Rosneft agreed to a share swap under which they would jointly explore for offshore oil and gas, in a deal that immediately raised concerns in the United States about Russia's global oil ambitions.

BP , recovering from its Gulf of Mexico oil spill, said on Friday it will swap 5 percent of its shares, valued at $7.8 billion, for 9.5 percent of Rosneft.

The deal, which is expected to be completed in a few weeks, highlights a sharp turnaround in relations with Moscow both for BP and its Chief Executive Bob Dudley, who was forced to flee Russia in 2008 after heading BP's Russian joint venture, TNK-BP, which is half-owned by BP.

Dudley had been the boss for TNK-BP's formation in 2003 and was forced to leave due to what he described as a campaign of harassment by BP-TNK's billionaire oligarch co-owners.

The issue has since been resolved and Dudley returned to Moscow for the first time this summer, following his appointment as CEO of BP, to be warmly welcomed by officials.

Tony Hayward, Dudley's predecessor who was vilified for his handling of BP's massive Gulf of Mexico spill in 2010, holds a seat on TNK-BP's board of directors.

Russia is a key part of BP's global operation, providing the company with a quarter of its reserves before the U.S. oil spill, so it is vital for Dudley to establish a good working relationship with the world's largest oil exporting nation.

Congressman Edward Markey, who is the top Democrat on the House Natural Resources Committee, immediately called for a review of the deal by U.S. regulators.

GLOBAL STAGE

Russia has increasingly been looking to raise its influence on the global financial stage, with major companies -- including state-controlled ones -- seeking foreign acquisitions.

Some deals have come under fierce opposition in the countries involved, such as Surgutneftegas's purchase of a stake in Hungary's MOL . Others, like Sberbank's bid for German carmaker Opel, collapsed.

Prime Minister Vladimir Putin's government has also pledged to ease investors' access into Russia as it looks to foreigners to play a key role in helping to modernize the economy -- including through taking part in a big privatization drive starting this year.

Britain's new coalition government has attempted to improve relations with Moscow -- tense since the murder of ex-KGB agent Alexander Litvinenko in 2006 -- although tensions resurfaced last month with the expulsion of a Russian diplomat from London.

U.S.-listed shares of BP, which had been trading higher, fell slightly to $48.87 in post-market trading. The stock had closed at $49.25 on the New York Stock Exchange.

(Additional reporting by Volodya Soldatkin, Toni Vorobyova and Darya Korsunskaya in Moscow and Kristen Hays and Chris Baltimore in Houston, writing by Anna Driver, editing by Gerald E. McCormick, Gary Hill)