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MOSCOW, Sept 11 (Reuters) - Russia is ready to continue to cooperate with the United States in fighting terrorism, President Dmitry Medvedev said on Thursday.

"The threat of terrorism is still there, the challenge has not been overcome," Medvedev told a meeting of top military officials. "Russia is ready for a coordinated cooperation with the United States and other states in fighting terrorism."

Medvedev made his remark in reference to the anniversary of the Sept. 11 attacks on the United States.

Medvedev's predecessor Vladimir Putin was among the first leaders to express his condolences to U.S. leaders after the Sept. 11 attacks pledging to work together in fighting terrorism.

The cooperation was thrown in doubt after Washington led international criticism of Russia's invasion of Georgia last month to crush Tbilisi's attempt to retake a pro-Moscow separatist province.

Russian top officials have said that by urging punitive action against Moscow, the United States was putting at risk bilateral cooperation in global issues like terrorism and proliferation of nuclear weapons.

"This (working with Russia against terrorism) is more useful that developing relations with rotten regimes," Medvedev said referring to the pro-Western government in Georgia. (Writing by Oleg Shchedrov, editing by Keith Weir)

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