MOSCOW, July 4 (Reuters) - Russia will grant President Barack Obama permission next week to ship U.S. weapons supplies across its territory, or through its airspace, en route to Afghanistan, sources on both sides told Reuters on Saturday.

The transit deal will open up an important corridor for the United States as it steps up its Afghan war against Taliban insurgents by sending in more troops. Routes via Pakistan have come under attack by militants.

It will be one of the main agreements signed during Obama's Moscow summit next week with Kremlin chief Dmitry Medvedev, the sources said.

"The agreement will include the transit of all U.S. goods, including military ones (to Afghanistan)," a senior Kremlin source told Reuters.

A U.S. source confirmed the deal would be signed and said it would mark a step forward in cooperation on Afghanistan, which Russia views as a key area where both the former Cold War foes can work together to mend ties.

It was not immediately clear if the deal would allow the United States to fly troops over Russian territory to Afghanistan.

Medvedev has repeatedly said he is ready to widen cooperation with U.S.-led coalition and NATO forces in Afghanistan, though Moscow has ruled out sending any of its own troops to fight.

Russia has already granted Washington the right to transit 'non-lethal' supplies, such as food, overland via Russia -- and Central Asia -- to Afghanistan.

Moscow has also granted NATO members Germany, France and Spain the right to use Russian territory to transit military cargos to Afghanistan. (Additional reporting by Washington bureau) (Reporting by Oleg Shchedrov and Guy Faulconbridge in Moscow, editing by Mark Trevelyan)

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