Russia hits back at US over Syria stance

* Russia says Clinton statement was "incorrect"

* Says her remarks go against what was agreed in Geneva (Adds quotes, background)

MOSCOW, July 6 (Reuters) - Russia hit back at U.S. criticism of its stance on the conflict in Syria on Friday, saying Washington's suggestion that Moscow should "pay a price" for helping keep President Bashar al-Assad in power was "incorrect."

Deputy Foreign Minister Gennady Gatilov told Interfax news agency that U.S. Secretary of State Hillary Clinton's statement went against the strategy for ending the bloodshed in Syria that was agreed by world powers last Saturday in Geneva.

Russia, which is sensitive about outside interference in any sovereign state, lobbied hard against efforts by other powers at the Geneva talks to include a precondition that would have excluded Assad from a proposed national unity government.

"The statement (by Clinton) was incorrect," Gatilov was quoted by Interfax as saying. "What worries us more than anything is that such remarks go against the final document of the Geneva talks, the adoption of which was approved with the participation of the U.S. secretary of state."

The United States is spearheading international efforts to pressure Russia into backing sanctions against its ally Syria and into helping facilitate Assad's exit from power.

Clinton's remark highlighted the gulf between Western and Arab countries, and Russia and China. Beijing and Moscow have in the past vetoed U.N. Security Council resolutions designed to put pressure on Assad. (Reporting by Alissa de Carbonnel, Editing by Timothy Heritage)