Carrying Ukrainian and Lithuanian flags, as well as slogans criticizing the Russian president, the picket participants chanted "Free Savchenko!".
Russia has accused Savchenko, 34, of correcting Ukrainian artillery fire during clashes with pro-Russian separatists in Eastern Ukraine in June of 2014. Two Russian journalists were killed in the exchange. If found guilty, Savchenko would face up to 23 years in prison.
Savchenko, who is held custody in the southern Russian city of Donetsk, pleaded not guilty. Savchenko denies all accusations and has refused to accept food and water after a court last Thursday adjourned its hearing where the defendant was to make her final statements.
One of the organizers of the protest in Vilnius, Conservative MP Mantas Adomėnas, said the Savchenko trial was an insult to law.
"This is a violation of international law and human rights, an insult to the concept of law when a soldier defending her country is on trial by the country she attacked," Adomenas told journalists.
His party fellow, diplomat Žygimantas Pavilionis, said the situation in Ukraine was similar to the 1991 January developments in Lithuania when the Soviets attempted to restore the Moscow influence by force.
Lithuania and four other countries have suggested that the European Union should make a so-called Nadiya Savchenko list, with sanctions for Russian officials who would be placed on the list for participating in Savchenko's persectuion.
Lithuanian Minister of Foreign Affairs Linas Linkevičius told BNS on Wednesday that "there should be certain consequences for the persons related to the fabricated case. A possibility of such list should be considered," said the minister.
According to him, the initiative is supported by ministers in of Sweden, Great Britain, Romania and Poland, who will shortly present the proposal to EU's foreign policy chief Federica Mogherini.
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