The Lithuanian Government revealed last month that it would be seeking the extradition of Mr Gecas for "participation in the killing of civilians and Jews in Lithuania and Belarus."
The head of the country's special investigations unit said it had sought a court order for the arrest of 85-year-old Anton Gecas, who has consistently denied involvement in atrocities.
Mr Gecas, who lives in Edinburgh, was alleged to have taken part in the mass murder of Jews and other civilians in Lithuania when it was occupied by the Nazis during World War Two.
Prosecutor Rimvydas Valentukevicius said that the order "would be one of the most important steps in seeking Gecas' extradition".
The Lithuanian Government revealed last month that it would be seeking the extradition of Mr Gecas for "participation in the killing of civilians and Jews in Lithuania and Belarus."
Mr Valentukevicius declined to say whether prosecutors had found new evidence against Mr Gecas since then, or whether they had finished drafting the charges.
"The application to court itself indicates that we believe we have enough evidence to bring Gecas to trial," he said.
Mr Gecas' lawyer, Edinburgh-based Nigel Duncan, said: "He will resist any attempt to extradite him to Lithuania or anywhere else.
"At the moment nothing has reached this country, and we just have to wait and see what happens if and when it does happen.
"His position is that he did not do what he is being accused of.
"The only comment I would make at the moment is that the Crown Office has already decided there was not sufficient evidence to warrant a prosecution under the War Crimes Act.
Failed libel action
"If, as the Lithuanian government are apparently saying, they have new evidence, then obviously we will want to look at that.
"At the moment we have no idea what they are talking about. We haven't been in contact with them."
Last February the Wiesenthal Centre, famous for its work hunting the perpetrators of the Holocaust, sent a file on Mr Gecas to the Lithuanian Government and demanded that he be put on trial.
The former mining engineer lost a libel action in 1992 against Scottish Television after it alleged that he had led atrocities against Jews in his native country and Belarus as the alleged head of a special police battalion.
Lengthy process
The Lithuanian move, made in the District Court in Vilnius on Monday morning, was the first stage in a lengthy process to secure the extradition of Mr Gecas.
It is expected that it will take at least two weeks to draw up the legal papers which can be presented to the British authorities.
It is also not clear if the papers are handed to the British Embassy in Vilnius to be passed onto the Foreign Office, or if the Lithuanian Embassy in London will receive them first.
However, once an extradition request is received the process would work like this:
If the extradition was to move forward, a number of appeals would be open Mr Gecas.
He could appeal against committal proceedings and the judgement, and then he could appeal against the ultimate decision of Scottish ministers.
In each case an appeal would be heard in the High Court.