* NATO chief urges Russia to stop destabilising Ukraine
* Rasmussen says NATO not discussing any military involvement
* NATO working on bolstering defences of eastern allies (Adds quotes from later press conference)
By Adrian Croft
LUXEMBOURG, April 15 (Reuters) - Russia is deeply involved in the crisis in eastern Ukraine, where pro-Moscow separatists have seized control of a number of government buildings, NATO Secretary-General Anders Fogh Rasmussen said on Tuesday.
The remarks from the head of the western military alliance underline rising tensions with Moscow, which says it is not involved in the armed pro-Russian protests in eastern Ukraine.
Asked if he had seen evidence of Russian involvement in events in eastern Ukraine, Rasmussen told reporters: "We never...comment on intelligence, but I think from what is visible, it is very clear that Russia's hand is deeply engaged in this."
Relations between NATO and Russia have turned icy since Russia annexed Ukraine's Crimea region last month. NATO, accusing Russia of massing forces on Ukraine's border, has also suspended cooperation with Moscow.
Rasmussen, in Luxembourg for talks with European Union defence ministers, called on Russia to "de-escalate the crisis, to pull back its troops from Ukraine's borders, to stop destabilising the situation in Ukraine and make clear that it doesn't support the violent actions of pro-Russian separatists."
"Russia should stop being part of the problem and start being part of the solution."
Military action by NATO, which is focused on protecting its own 28 members from Poland to Canada, is not on the agenda.
Rasmussen said NATO was not discussing military involvement in non-NATO member Ukraine and wanted to strengthen the defences of eastern European allies nervous about Russia's intentions.
Rasmussen said later that whether to send military supplies to Ukraine would be a decision for NATO member governments, rather than NATO itself, to make.
"Military equipment is possessed by individual nations, by individual allies, and not by NATO. NATO is not engaged in that. So that is based on bilateral agreements between Ukraine and individual allies," he said.
An adviser to U.S. Secretary of State John Kerry said in Berlin on Monday that the United States was considering supplying arms to Ukraine.
White House spokesman Jay Carney said later however that the United States was not "actively considering" lethal aid for Ukraine but was reviewing the kinds of assistance it could provide.
NATO ambassadors are expected on Wednesday to discuss options put forward by military planners for reinforcing the defences of eastern allies through exercises and temporary deployments of planes and ships sent by other allies.
Rasmussen declined to comment in detail on what reinforcement measures NATO might take but said some suggested measures could be implemented immediately while others could be decided on at a later stage taking account of how the Ukraine situation develops.
In his talks with EU defence ministers, Rasmussen said he would call for stronger cooperation between NATO and the EU, proposing that the military rapid reaction forces that both organisations maintain should train and exercise together more often. (Reporting by Adrian Croft; Editing by Giles Elgood and Angus MacSwan)