* NATO, Russia to meet for first time since March
* Developments could point to slight easing of tension
* NATO chief urges Russia to stop supporting "pro-Russian gangs" (Adds U.S. State Department comment, paragraph 8)
By Andrius Sytas
VILNIUS, May 30 (Reuters) - Russia is in the process of pulling back around two-thirds of the troops it had close to the border with Ukraine, NATO Secretary-General Anders Fogh Rasmussen said on Friday, a far more significant withdrawal than NATO has previously estimated.
Rasmussen also announced that ambassadors from Russia and NATO countries would meet in Brussels on Monday for the first time since March 5, soon after Moscow provoked the worst East-West crisis since the Cold War by seizing Ukraine's Crimea region.
Taken together, the two announcements could point to a slight easing of tensions between the Western military alliance and Russia over Moscow's annexation of Crimea and what NATO sees as Russian interference in eastern Ukraine.
NATO suspended all practical cooperation with Russia in April to protest its annexation of Crimea, but left the door open to contacts at ambassadorial level or higher in order to allow the two sides to discuss ways out of the crisis.
Monday's meeting is expected to discuss the security situation in and around Ukraine, a NATO official said.
"We have seen signs of at least a partial withdrawal. Our estimate is that around two-thirds of Russian troops have been or are being pulled back," Rasmussen told Reuters on the sidelines of a meeting of the NATO Parliamentary Assembly in the Lithuanian capital Vilnius.
Rasmussen's assessment was in line with earlier comments by a U.S. defence official that Russia had withdrawn most of its troops from the Ukrainian border, but that seven battalions, amounting to thousands of men, remained.
In Washington, a State Department spokeswoman told a regular briefing: "We continue to observe Russian troop activity in the vicinity of the border with Ukraine. Over two-thirds of the troops have now pulled back from the border.
"Several thousand troops still remain in the vicinity, but most of these units appear to be preparing to withdraw," she said. "Some units continue to be capable of operations at short notice."
NATO estimated that, at the peak, Russia had around 40,000 troops massed close to the Ukraine border. A NATO military officer said on Wednesday that thousands of them had withdrawn, but tens of thousands remained.
SUBSTANTIAL FORCE REMAINS
Despite the withdrawal, Rasmussen said that Russia still had substantial forces along the Ukrainian borders that were ready to intervene if ordered to do so by Moscow.
"We welcome what we have seen but we continue to urge Russia to pull back all troops from the Ukrainian border," Rasmussen told Reuters.
In comments to a Lithuanian broadcaster, Rasmussen called on Moscow to "stop supporting armed pro-Russian gangs and seal the border so that we don't see arms and fighters crossing into Ukraine."
Ukraine's government said on Friday it would press ahead with a military offensive against separatists despite a deadly attack on an army helicopter amid reports that fighters from Russia have been involved in rebellions in the east.
Answering questions from members of the NATO Parliamentary Assembly, made up of national members of parliament from the 28 NATO states, Rasmussen said NATO must adapt to the new kind of warfare Russia had practiced in Ukraine, which he said included covert military operations and disinformation campaigns.
All or part of NATO's rapid reaction force, the NATO Response Force, should be on very high alert and ready to deploy very quickly, and the role of allied special operations forces would be even more important in future, Rasmussen said. (Reporting by Andrius Sytas; Additional reoporting by Arshad Mohammed in Washington; Writing by Adrian Croft; Editing by Barbara Lewis and Jonathan Oatis)