Dr Efraim Zuroff, director of the Wiesenthal Centre in Jerusalem, said it had been seeking the extradition of Anton Gecas for 14 years.
However, he voiced concern that the announcement would give 85-year-old Mr Gecas, who lives in Edinburgh, advanced warning and would allow him more time to prepare his case.
Mr Gecas has not commented on confirmation from Lithuanian prosecutors that an application would be made for his enforced return to the country.
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.
Dr Zuroff said: "We are very pleased that Lithuania intends to seek his extradition but I am a bit concerned that Gecas might run away.
"There is nothing to stop him from running away.
"The announcement is a bit strange because why would the government let Gecas know that such a step is imminent?"
However, Dr Zuroff, who remained "hopeful" that extradition would proceed, said: "I have been working on this case for 14 years and I cannot think of a happier event than to go to Vilnius (the Lithuanian capital) and see Gecas in a courtroom."
Rimvydas Valentukevicius, head of the department of Special Investigations in the Lithuanian Prosecutor General's office, said he could not speculate on exactly when an approach to the Home Office asking for extradition would be made.
He added that the country's archive service would be asked to provide more information on the charges.
War crimes group
Mr Gecas's wife Astrid, speaking at their home, said the former mining engineer had no comment to make.
The Crown Office said it had yet to receive a formal request for extradition, while the Home Office said it could not confirm or deny the details of any request received from other states.
The moves by Lithuania were also welcomed by Lord Janner, secretary of the parliamentary all-party war crimes group, who said he would be "surprised" if Mr Gecas was not extradited.
He said: "What's happened now is that the Lithuanians have said we have got new evidence.
"And on this evidence added to the evidence we had before, we consider that there is sufficient to warrant prosecuting this man and we are going to ask for him to be extradited."
Mr Gecas 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.
Lord Milligan, at the Court of Session in Edinburgh, said in his judgement that he was "clearly satisfied" Mr Gecas had taken part in a number of killings and "committed war crimes against innocent civilians".
Lord Milligan said it had been proved that Mr Gecas was a platoon commander of the 12th Auxiliary Police Services Battalion.
The allegations were investigated by Scottish prosecution authorities, but no action was taken against Mr Gecas.
A Crown Office spokeswoman said: "At the close of those inquiries a decision was taken that proceedings could not be taken on the evidence available at that time," she said. "The case does remain open."