BRUSSELS, Belgium — Russia has halted all military cooperation with NATO, the Western alliance said yesterday, in the latest sign of East-West tension over the invasion of Georgia.

An Alliance spokeswoman, Carmen Romero, said NATO had received notification through military channels that Russia’s Defense Ministry had taken a decision “to halt international military cooperation events between Russia and NATO countries until further instructions.”

America immediately played down the significance of the Russian decision, saying that NATO had already effectively frozen cooperation in protest at Russia’s continued military presence in much of Georgia.

“For all practical purposes, military-to-military cooperation had really already been ended with the Russians,” said a U.S. National Security Council spokesman, Gordon Johndroe, with vacationing President Bush in Crawford, Texas.

“I can’t imagine a circumstance right now that we would engage in military cooperation with the Russians until the situation in Georgia is resolved.”

In a move that angered Russia, NATO foreign ministers on Tuesday said they would make further ties with Russia dependent on Moscow making good on a pledge to pull its troops back to pre-conflict positions in Georgia. But they stopped short of calling an immediate halt to all cooperation.

Moscow has also bristled at NATO’s insistence that Georgia could one day join the alliance and by an agreement signed Wednesday allowing America to base anti-missile interceptors in Poland.

The American State Department called the Russian move “unfortunate.” A spokesman, Robert Wood, told reporters in Washington “we want Russia to work with us” despite American concerns about the Georgian invasion.