MOSCOW/WASHINGTON, Jan 26 (Reuters) - Russia and the United States have struck a deal to extend the New START nuclear arms control treaty, the Kremlin said on Tuesday, a move that preserves the last major pact of its kind between the world's two biggest nuclear powers.

The treaty, which was due to expire next month, limits the number of strategic nuclear warheads, missiles and bombers that Russia and the United States can deploy.

The Kremlin declared the breakthrough, which was widely anticipated, in a statement announcing that President Vladimir Putin and U.S. President Joe Biden had spoken for the first time since Biden took office last week.

Moscow and Washington had failed to agree an extension under former U.S. President Donald Trump, whose administration had wanted to attach conditions to a renewal that Moscow rejected.

The Kremlin said the two leaders had "expressed satisfaction" that diplomatic notes between the two countries had been exchanged earlier on Tuesday confirming the agreement would be extended.

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It said that the necessary procedures required for the pact to come into force before it expires on Feb. 5 would be completed in the coming days.

"The extension is in the interest of both countries, as well as the whole world," Kremlin spokesman Dmitry Peskov had told reporters on a conference call earlier on Tuesday.

Signed in 2010, the New START (Strategic Arms Reduction Treaty) is widely regarded as a cornerstone of global arms control.

The White House said last week that Biden would seek a five-year extension to New START, something the U.S. disarmament ambassador said would be just the beginning of efforts to engage Moscow.

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"This extension makes even more sense when the relationship with Russia is not at a good stage," Robert Wood told the Conference on Disarmament in Geneva on Tuesday.

Russia's ambassador to the United Nations in Geneva, Gennady Gatilov, said earlier on Tuesday that the pact's extension would give Moscow and Washington more time to work jointly on other international security issues.

The Kremlin said in the same statement that Putin had told Biden a normalization of relations between Moscow and Washington would be in both countries' interests.

It said the two leaders had also discussed the U.S. decision - during Trump's administration - to exit the Open Skies treaty, as well Iran's nuclear program and the conflict in Ukraine. (Additional reporting by Dmitry Antonov, Maria Kiselyova, Polina Devitt and Darya Korsunskaya; Additional reporting by Emma Farge and Stephanie Nebehay in Geneva; Writing by Gabrielle Tétrault-Farber; Editing by Andrew Osborn and Mark Heinrich)