The Western alliance's latest statements came as Moscow heaped even more pressure on Ukraine's teetering economy with a painful gas-price hike, undermining what had been tentative signs of a calming in the worst East-West standoff since the Cold War.
Ukraine's parliament met one of Moscow's key demands by voting unanimously to disarm all self-defence groups that sprang up across the country during its political crisis, which first erupted in late November over the then-government's decision to ditch a landmark EU alliance.
He added however that "diplomatic lines of communication" remained open.
Rasmussen warned he could not confirm Russia had pulled away from the Ukrainian border.
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"This is not what we have seen," he said as NATO foreign ministers gathered for two days of talks, including US Secretary of State John Kerry, who flew into Brussels between shuttle diplomacy stops in the Middle East.
Ukraine and the United States have accused Russia of massing thousands of troops near the border and have expressed concern that Moscow plans to seize southeastern parts of Ukraine that are home to large populations of ethnic Russians.
Ukraine also reported yesterday that Russian troops were leaving the sensitive area, adding it appeared to coincide with a phone call that Putin had unexpectedly placed to US President Barack Obama on Friday.
With the assurances from Moscow, NATO stepped back from a floated idea to reinforce the alliance's military presence in countries bordering Russia, preferring for now to suspend cooperation and give more time to talks.