Moscow is pressing Nato to explain its plans to enhance its military presence in Eastern Europe, Russian Foreign Minister Sergei Lavrov has said.
"We not only expect answers, but answers... based fully on respect for the rules we agreed on," he said.
But Nato Secretary General Anders Fogh Rasmussen denied the alliance had broken an agreement with Moscow.
He also accused Russia of "violating every international commitment it has made" by annexing Crimea.
Nato has said it will continue to carry out "collective defence" to protect member states and it has reinforced defences in Eastern Europe.
The alliance has also halted all civilian and military co-operation with Russia.
The Nato chief said he had not received any questions from Moscow and called Russian accusations about the alliance's actions "propaganda and disinformation".
In response, Russia has recalled its top military representative at Nato in Brussels for "consultations" in Moscow.
"We don't see an opportunity to continue military cooperation as usual with Nato," Deputy Defence Minister Anatoly Antonov said on Thursday.
Mr Rasmussen has previously described Russia's annexation of Crimea as the gravest threat to European security for a generation.
At a summit in Brussels, the alliance expressed concerns over a massive build-up of Russian troops on Ukraine's eastern border, amid fears of an invasion.
The European aviation safety watchdog has also warned of "serious risks to the safety of international civil flights" above Crimea and told airlines to avoid the airspace.
The European Aviation Safety Agency said Russia's stated intention of taking over air traffic control above the annexed region, which is currently controlled by Ukraine, had led to an "unsafe situation."
Nato planners are currently looking at options including situating permanent military bases in the Baltic states to reassure members in Eastern Europe.
Russia's actions in Ukraine have caused concern in Estonia, Latvia and Lithuania - all Nato members which were part of the Soviet Union during the Cold War.
Nato jets will take part in air patrols in the region later in a routine exercise that analysts say has taken on added significance because of the crisis. Several Nato countries, including the UK, US and France, have offered additional military aircraft.
But Mr Lavrov accused Nato of exaggerating the importance of Russian troop movements on the borders of eastern Ukraine.
He said Russia had the right to move troops within its territory, and that the forces currently near the border would return to their permanent bases after completing military exercises.
Moscow also announced that some of its special forces would be taking part in a joint military exercise in Belarus later this month.
Russia's defence ministry said a unit of its paratroopers will join their Belarusian counterparts to rehearse assault operations from 15-18 April in the north of the country.
Meanwhile, Germany's ambassador to Russia was summoned by the Russian foreign ministry on Thursday after Finance Minister Wolfgang Schaeuble likened Moscow's moves in Crimea to Adolf Hitler's 1938 annexation of German-speaking regions of Czechoslovakia.
"We consider such pseudo-historical references by the German minister provocative," the Russian foreign ministry said in a statement. "The comparisons by him are a gross manipulation of historic facts."
Nato membership over time