BRUSSELS - NATO on Tuesday said it could not confirm the withdrawal of Russian troops from near the flashpoint Ukrainian border as Russia heaped even more pressure on a teetering Ukraine economy with a painful gas price hike.

Foreign ministers from the western alliance gathered in Brussels to try and forge a response to Russia annexation of Crimea last month, amid 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 that first erupted over a ditched EU alliance in late November.But tensions still remained high over two weeks after Moscow formally annexed Crimea and NATO Secretary General Anders Fogh Rasmussen warned he could not confirm that Russia had pulled away from the Ukrainian border, as announced by the Kremlin.

"This is not what we have seen," Rasmussen said as NATO ministers gathered for two days of talks, including US Secretary of State John Kerry, who flew in 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 intends to seize southeastern parts of Ukraine that are home to large populations of ethnic Russians, following the Crimea takeover.

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

Ukraine also reported Monday 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 seemed to be stepping back from a floated idea to reinforce the alliance's military presence in countries bordering Russia, preferring for now to 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 with Russia. The move would be highly controversial for Moscow, reversing an informal agreement made when NATO expanded east to include former Warsaw Pact countries that were eager to break away from years of Soviet domination.

Meanwhile, the United States has asked to boost the number of troops and aircraft it has stationed at an airbase in NATO ally Romania, President Traian Basescu said on Tuesday, as tensions between the West and Russia simmer over neighbouring Ukraine.

US forces have used the Mihail Kogalniceanu air base on the Black Sea in eastern Romania since 1999. It is a major hub for US troops leaving Afghanistan and is located not far from Ukraine's Crimea peninsula, annexed last month by Russia.

Russian President Vladimir Putin on Tuesday promised a top Tatar official in Russia he would consider rehabilitation for the Crimean Tatars, a painful issue for a people deported under Stalin.

Putin made the comment in a meeting with Rustam Minnikhanov, the president of the Russian republic of Tatarstan on the Volga which is thousands of kilometres from Crimea but whose Tatar population are close ethnic kin of the Crimean Tatars.

Minnikhanov, who has travelled to Crimea after its annexation by Russia, asked Putin to consider the Crimean Tatars a "repressed people" subject to rehabilitation under an earlier Russian law.

"It would be nice if the Crimean Tatars were considered... under the 1991 law," Minnikhanov said. "It would be serious moral support to the Crimean Tatars."

The cautious line could come as a disappointment to eastern NATO members - such as the Baltic nations and Poland - who were expected to argue for a tougher stance against Russia at the meeting.

Poland "would welcome any forces" on its territory, Foreign Minister Radoslaw Sikorski said.

Ahead of the NATO talks, Germany's foreign minister said that he saw no quick solution to the crisis, nor the likelihood of Ukraine joining NATO.

"We can't promise we'll be in a position to resolve this conflict in the short term," Frank-Walter Steinmeier said.

Ukraine is not a NATO member but it did form a "distinctive partnership" with the Alliance in 1997 and has been staging joint exercises with its state members ever since.

Parliament in Kiev on Tuesday approved a new series of joint military exercises with the alliance that would put US troops in direct proximity with Russian forces in the annexed Crimea peninsula.

"This is a good opportunity to develop our armed forces," acting Defence Minister Mykhailo Koval said.

The exercises would partly occupy a 25-day span between July and October based around two Odessa ports and "along the waters of the Black Sea".

Meeting a key demand posed by Russia, Ukraine's parliament Tuesday also voted to disarm all self-defence groups that had sprung up across the country during its political crisis.

The move came after a member of the radical Ukrainian nationalist group Pravy Sektor opened fire in central Kiev late Monday, injuring three.

The crisis is at an especially critical juncture in Kiev as Ukrainian politicians jockey for position ahead of May 25 presidential elections after the fall of president Viktor Yanukovych.

And with Moscow able to use gas as a lever, Gazprom chief executive Alexei Miller said Ukraine will now pay $385.5 dollars per 1,000 cubic metres of gas from the previous cut rate of $268.5.

"The discount will no longer apply," he said in a statement. "This is due to the inability of the Ukrainian side to pay for debts from 2013 and realise full payments for current deliveries."

The discount had been agreed between Yanukovych and President Vladimir Putin in December 2013 as a form of financial aid to the former regime.

The price hike - although widely expected - is a new blow to the Ukrainian economy which needs an international rescue to stave off the risk of default.