Landsbergis told the Ziniu Radijas radio station that he contacted his Greek counterpart on Wednesday to "inform him about the importance of this man both for our legal system and for our history" and likened the situation to the Nuremberg trials of former Nazi leaders after World War Two.
"I compared the situation, perhaps not necessarily correctly, with the Nuremberg case, when the Western world was on the hunt for those who organized crimes against humanity during World War Two," the minister said.
"I said this is a Lithuanian Nuremberg case. In fact, we have one of the biggest crimes committed against our people, and we are likewise trying to find the organizers of it all over the world," he said.
"One of them is in Greece today. I hope that this will be taken very seriously and the man will be returned to us," the minister added.
Lithuanian officials said on Wednesday that Alexander Radkevich, a Ukrainian citizen convicted in the so-called January 13 case, had been detained in Greece.
He was detained back in mid-September, but it took time to ascertain his identity, they said.
The 15min.lt news website has reported that Radkevich, 53, was sentenced to four years in prison for driving a tank involved in the events at the Lithuanian capital's Press House.
Radkevich is one of 67 people handed prison sentences in the mass trial.
Fourteen civilians were killed and hundreds more were wounded when the Soviet troops stormed the TV Tower and the Radio and Television Committee building in Vilnius in the early hours of January 13, 1991.
The Soviet Union used military force in its attempt to remove the legitimate government of Lithuania which declared independence on March 11, 1990.