NATO says it has suspended all co-operation with Russia over the Crimea crisis and is questioning Moscow’s claim to have withdrawn troops from near the Ukrainian border.

The Western alliance’s latest statements came on Tuesday 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 has 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 erupted in late November over the then-government’s decision to ditch a landmark EU alliance.

But tensions remain high more than two weeks after Moscow formally annexed Crimea, and NATO Secretary General Anders Fogh Rasmussen says the alliance is “suspending all practical co-operation with Russia, military and civilian”.

He says however that “diplomatic lines of communication” remain open.

Rasmussen also warned on Tuesday that he could not confirm Russia had pulled away from the Ukrainian border.

“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.

Ukraine and the United States have accused Russia of massing thousands of troops near the border and have expressed concern Moscow plans to seize southeastern parts of Ukraine that are home to large populations of ethnic Russians.

German Chancellor Angela Merkel’s office said Russian President Vladimir Putin had personally informed her of the troop pullback in a phone conversation and on Tuesday said she had “no reason” to doubt his word.

Ukraine also reported on Monday that Russian troops were leaving the sensitive area, adding it appeared to coincide with a phone call 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 co-operation and give more time to talks.

“I think everybody realises that the best way forward is a political and diplomatic dialogue,” Rasmussen said, though he added NATO was “very determined to provide effective defence and protection of our allies”.

One counter-measure apparently off the table for now is the idea to set up permanent military bases in NATO countries bordering Russia.

The move would be highly controversial for Moscow, reversing an informal agreement made when NATO expanded east to include former Warsaw Pact countries eager to break away from years of Soviet domination.

But Dutch Foreign Minister Frank Timmermans said that for now “we don’t need NATO troops at the border with Russia,” adding there was “no need for sudden moves”.

Eastern NATO members – such as the Baltic nations and Poland – want a tougher stance against Russia and would welcome a deeper NATO presence within their borders.

In a joint statement, ministers confirmed that military and civilian co-operation between NATO and Russia was suspended, but said projects in Afghanistan would remain and diplomatic channels were still open.

Rasmussen added that joint efforts to fight narcotics traffic in Afghanistan would continue.

The crisis is at an especially critical juncture in Kiev as Ukrainian politicians jockey for position ahead of May 25 presidential elections.

And with Moscow able to use gas as a lever, Gazprom chief executive Alexei Miller says Ukraine will now pay $385.5 dollars per 1000 cubic metres of gas from the previous cut rate of $268.5.