By Robin Emmott

BRUSSELS (Reuters) - Russia accused the United States on Wednesday of intimidation by sailing a U.S. naval destroyer close to Russia's border in the Baltics and warned that the Russian military would respond with "all necessary measures" to any future incidents.

Speaking after a meeting between NATO envoys and Russia, their first in almost two years, Moscow's ambassador to NATO said the April 11 maritime incident showed there could be no improvement in ties until the U.S.-led alliance withdrew from Russia's borders.

"This is about attempts to exercise military pressure on Russia," the envoy, Alexander Grushko, said. "We will take all necessary measures, precautions, to compensate for these attempts to use military force," he told reporters.

U.S. Ambassador to NATO Douglas Lute pressed Russia about the incident, warning it had been dangerous. The United States has said the guided missile destroyer USS Cook was on routine business near Poland when it was harassed by Russian jets.

"We were in international waters," a NATO diplomat reported Lute as telling Grushko during the NATO-Russia council meeting.

Despite what officials said was a calm and professional meeting, the public comments highlighted the state of tension that persists between the sides since Moscow's annexation of Ukraine's Crimea in March 2014 and its support for separatist rebels in eastern Ukraine.

NATO Secretary-General Jens Stoltenberg said the NATO member states had, during the meeting, rejected Grushko's account of the crisis in eastern Ukraine, where 9,000 people have died since April 2014.

Stoltenberg said while there were "profound disagreements" over how to handle Europe's security, each side urgently needed to talk more and to use existing rules to reduce military risk.

Stoltenberg suggested revamping a Cold War-era treaty known as the Vienna document, which sets out the rules for large-scale exercises and other military activity, as well as telephone hotlines and other military communication channels.

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"We have to use our lines of communication," he said.

Russia's chief concern is NATO's biggest modernization since the Cold War, which is likely to include a military build-up in eastern Europe with a rotating, multinational force in Poland and the Baltics.

NATO says the plans are a proportionate response to Russian aggression following Moscow's annexation of Crimea, and the alliance had no forces in eastern Europe before the Ukraine crisis.

Poland and other NATO members in the Baltics worry about an increase in the Russian military presence in its Kaliningrad enclave, where Russia is positioning longer-range surface-to-air missiles.

NO AGREEMENT ON UKRAINE

The session of the NATO-Russia Council, which last met in June 2014, had been called in part to assuage Russia's concerns that it feels threatened by NATO. But core differences clearly remained afterwards.

NATO envoys had expressed concern about Russia's so-called snap exercises, where thousands of Russian troops carry out war games without any prior warning. "That is clearly destabilizing," a NATO diplomat said.

Stoltenberg said NATO members had rejected Grushko's description of the crisis in eastern Ukraine as a civil war.

"In the meeting, it was re-confirmed that we disagree on the facts, on the narrative and the responsibilities in and around Ukraine," Stoltenberg said after the meeting.

"Many allies disagree when Russia tries to portray this as a civil war. This is Russia destabilizing eastern Ukraine, providing support for the separatists, munitions, funding, equipment and also command and control," he said.

"So there were profound disagreements," he said.

Russia denies any direct involvement in eastern Ukraine.

(Reporting by Robin Emmott; Editing by Richard Balmforth)