* NATO to draft measures to beef up defences in eastern European
* Voices concern over Russian troops near Ukrainian border
* Russia's Lavrov says force will withdraw after war games (Adds context, NATO's response)
By Thomas Grove
MOSCOW, April 3 (Reuters) - Russia said on Thursday it wanted answers from NATO on its activities in eastern Europe after the Western military alliance promised to beef up defences for its eastern members.
Russia's annexation of Ukraine's Crimea region last month has caused the deepest crisis in East-West relations since the Cold War, leading the West to impose sanctions and sparking fear President Vladimir Putin has territorial designs beyond the Black Sea peninsula with its Russian-majority population.
NATO has ordered military planners to draft measures to reassure nervous Eastern European countries - which were under Moscow's domination until the 1989 end of the Cold War - but stopped short of calls by Poland to base more forces there.
Russian Foreign Minister Sergei Lavrov said any increase in NATO's permanent presence in eastern Europe would violate a 1997 treaty on NATO-Russian cooperation.
"We have addressed questions to the north Atlantic military alliance. We are not only expecting answers, but answers that will be based fully on respect for the rules we agreed on," Lavrov told reporters at a briefing with his Kazakh counterpart.
Foreign ministers from the 28-nation, U.S.-led NATO met this week to discuss responses to Russia's Crimea takeover, including sending NATO soldiers and equipment to allies in eastern Europe, holding more exercises, ensuring NATO's rapid-reaction force could deploy more quickly, and reviewing NATO's military plans.
Military planners will come back with detailed proposals within weeks, a NATO official said.
NATO military chiefs are concerned that an estimated 40,000 Russian forces near the Ukrainian border may signal plans by Putin to move beyond Crimea into eastern and southern Ukraine, which also have significant Russian-speaking populations.
Russian forces seized Crimea after mass protests toppled Ukraine's pro-Russian president. Moscow denounced this as a coup driven by right-wing extremists and said it reserved the right to protect Russian speakers in Ukraine, but denied having any intention to move into other areas of the ex-Soviet republic.
Lavrov responded to criticism over the size of the force along Russia's border with Ukraine by saying Moscow had the right to move troops on its territory and they would return to their permanent bases after military exercises.
He did not give a timeline for when war games would end but said NATO's concerns were overblown.
"It is necessary to de-escalate rhetoric which overshoots the mark and crosses into the unreasonable," he said. (Reporting by Thomas Grove and Alissa de Carbonnel in Moscow and Adrian Croft in Brussels, editing by Mark Heinrich)