"She was granted international protection and refugee status because she faces danger in her homeland," Lithuania's Deputy Interior Minister Elvinas Jankevicius told AFP yesterday but declined to elaborate.
Human rights activists have repeatedly accused Russian President Vladimir Putin of seeking to stamp out all visible dissent. The small liberal opposition often must choose between exile or repression, they add.
Kalmykova said she was charged with violating public rallies regulations, facing up to five years in prison, and was worried that authorities may open another criminal case against her.
"From Ukraine we went on to Lithuania. They (Russia) have already sent a notice on me to Interpol," she added in a telephone interview.
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A former businesswoman, Kalmykova is among over a dozen Russian citizens who have been granted asylum in the Baltic EU state in recent years.
A nation of three million, Lithuania is among the most hawkish NATO and EU members on Russia, and has called for tougher sanctions for Moscow's intervention in Ukraine.
Analysts say changes are highly unlikely after upcoming parliamentary elections in September, pointing to the divisions within the opposition and Kremlin's apparent readiness to tighten the screws even further.