Ukraine's parliament Tuesday met a key demand of both Russia and the West by voting to disarm self-defense groups that sprang up during months of deadly protests against Kiev's pro-Kremlin regime.

The decision came in the wake of a nighttime police raid on the central Kiev hotel headquarters of a far right nationalist organization that was instrumental in the February rise to power of a new team of pro-European leaders who are seeking to end decades of Russian dominance over the ex-Soviet state.

Russian gas giant Gazprom on Tuesday announced it was ending a gas discount enjoyed by Kiev in a major blow for the Ukrainian economy, as NATO foreign ministers prepared to forge a response to Russia's intervention in Crimea.

Ukraine on Monday reported a partial withdrawal of Russian troops from its eastern border amid growing signs that the Kremlin is ready to defuse the worst East-West standoff since the Cold War.

Ukraine's parliament on Tuesday approved a series of joint military exercises with NATO countries that would put U.S. troops in direct proximity to Russian forces in the annexed Crimea peninsula.

"This is a good opportunity to develop our armed forces," acting defense minister Mykhailo Koval told Verkhovna Rada lawmakers ahead of the 235-0 vote.

A U.S. aid package to Ukraine that also imposes sanctions on Russia for its Crimea takeover is expected to clear Congress Tuesday and head to President Barack Obama, ending a weeks-long impasse.

But there is already concern that the delayed legislation might be too little too late to have a substantial impact on resolving the most serious East-West confrontation since the end of the Cold War.

NATO foreign ministers will gather in Brussels on Tuesday as the defense alliance seeks to reinforce its eastern frontier against a resurgent Russia emboldened by the annexation of Crimea.

In a regular two-day meeting of the 28 ministers, including U.S. Secretary of State John Kerry, NATO will confirm the suspension of cooperation with Moscow, a decision made on March 5 after Russian troops grabbed Crimea from Ukraine.

The United States said Monday it would welcome any Russian move to pull its forces back from the Ukrainian frontier, but did not confirm reports that it has begun to do so.

"If reports that Russia is removing some troops from the border region are accurate, it would be a welcome preliminary step," U.S. State Department spokeswoman Jen Psaki said.

A hail of gunfire rings out as a group of soldiers leap from a helicopter, do a combat roll, crouch and open fire.

Running through a haze of smoke, clambering up and down ropes and engaging in hand-to-hand combat: Ukraine's newly-formed National Guard is hard at work learning to defend the crisis-hit country.

Russian President Vladimir Putin informed German Chancellor Angela Merkel on Monday about the partial withdrawal of troops he ordered from a region on the border with Ukraine, her office said.

"Moreover the two discussed further possible steps to stabilize the situation in Ukraine and Transdniestr," Moldova's largely Russian-speaking breakaway region, Merkel's spokesman Steffen Seibert said in a statement.

Ukraine's defense ministry said on Monday it has noticed a gradual withdrawal of Russian troops from its border that may be linked to Washington's latest push for a diplomatic solution to the worst East-West crisis since the Cold War.

"In recent days, the Russian forces have been gradually withdrawing from the border," the Ukrainian defense ministry's general staff spokesman Oleksiy Dmytrashkivskiy told Agence France Presse in a telephone interview.

Prime Minister Dmitry Medvedev visited Crimea on Monday, the first Russian leader to travel to the Black Sea region after Moscow seized it from Ukraine.

"Am in Simferopol. Today the government will discuss the development of Crimea," Medvedev wrote on Twitter.