NATO said Friday it has seen signs Russia is pulling troops back from its Ukraine border and announced its first talks with Moscow since its disputed annexation of Crimea.

"We have seen some signs of a start of Russian withdrawal," the alliance's outgoing Secretary General Anders Fogh Rasmussen said in Vilnius.

"Maybe around two thirds have now pulled back."

US Secretary of State John Kerry said earlier the troops -- estimated by NATO to number 40,000 -- were pulling back, days after Russian President Vladimir Putin announced they were to return to bases after the end of spring exercises.

Their presence had raised deep concerns after Moscow annexed Crimea in March and pro-Moscow rebels launched an ongoing uprising in eastern Ukraine.

In a further sign of a thaw in relations with Russia, Rasmussen on Friday announced a NATO-Russia Council would be held in Brussels next Monday.

The meeting between officials from the 28 member countries of NATO and Russia to will be the first since early March, when the Kremlin annexed Ukraine's Black Sea peninsula of Crimea and sparked an armed uprising in the east.

As parts of the separatist rust belt plunged further into anarchy Friday, Rasmussen also urged Russia not to meddle in the region -- something Moscow staunchly denies.

"We continue to call on Russia to stop supporting armed pro-Russian gangs and seal the border, so that we don't see arms and fighters crossing into Ukraine," he said.

He also vowed that NATO would boost cooperation with Ukraine.

"You will see in the future a strengthened cooperation between NATO and Ukraine, also when it comes to military cooperation," he said.

Ukraine is part of the alliance's Partnership for Peace programme, focussed on building ties with countries that were once within the Soviet sphere of influence.

Rasmussen said Kiev had forwarded the alliance a list of ways it could help, including by modernising their armed forces.

NATO itself does not have the resources to provide Kiev with military hardware but could make arrangements with member states.

"When it comes to the delivery of equipment it is a bilateral arrangement between the Ukrainian government and individual NATO allies," Rasmussen said.