The parliamentary amendment follows calls from the Central Board of Jewish Communities, the group's president David Saltiel told AFP.
"This is a moral victory," and a "fresh step forward in the recognition of the history of the Holocaust and of Greek Jews," he said.
In 2011 Greece recognized the right of Jewish survivors of the World War II Nazi Holocaust to gain back the nationality they had lost if they left the country, Saltiel said.
The new amendment concerns relatives of those survivors, many of whom live in Israel.
Thursday's vote passed largely unnoticed but has since become a political controversy.
The leftist Greek government on Saturday sharply criticized the opposition conservative New Democracy (ND) party for abstaining from the vote.
The ND countered that it backs the measure and attributed its abstention to confusion during the voting.
As expected the neo-Nazi Golden Dawn party, the fourth biggest in parliament, voted against the legislation.
Before the Nazi occupation, there were over 50,000 members of Greece's largest Jewish community in the second city Thessaloniki.
Eighty percent of the Jewish community in Greece were slaughtered during the war and now stands at less than 5,000 people.
In January the Jewish community in Thessaloniki finally got the go-ahead to build a Holocaust museum partly funded by Germany....
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Greece probing how parcel bombs got to France,
Germany
The investigation so far suggests that the booby-trapped mail sent to the IMF and the German Finance Ministry — presumably by a far-left group called the Conspiracy of Fire Nuclei — failed to raise an alarm because it contained only a small amount of gunpowder.
“The analysis so far... is that it was a small amount of gunpowder of the same type used in firecrackers...there was no detonator,” Greek Police Minister Nikos Toskas told Skai TV on Friday, citing evidence from investigators in France and Germany.
“Clearly they are from the same source, the same organization... the leftovers of the Nuclei,” which was dismantled by the police in 2011, he added.
Toskas defended the screening procedures at Athens airport, saying the equipment was recently purchased from Germany and is “the best in Europe.”
“The main screening is done before the plane is loaded, and this is where our investigation is focused,” he said, adding that there was “no sign” that additional parcels were sent.
The Conspiracy of Fire Nuclei is “likely behind” the Paris attack, a Greek police source told AFP, adding that French investigators had told their Greek counterparts that the letter was sent from Athens.
Separately, a source close to the French inquiry said it was focusing on “an anarchist group.”
Fragments of Greek stamps were found at the IMF offices where the mail bomb exploded, injuring a secretary’s face and hands.
Citing police sources, the Greek daily Avgi said the intended recipient was the IMF’s Europe director, Jeffrey Franks.
In a further twist, the names of two senior officials in the conservative New Democracy party of Greece were used as the alleged senders.
Toskas acknowledged that the incidents would require a “re-evaluation” of procedures in Greece and abroad.
IMF chief Christine Lagarde denounced a “cowardly act of violence” and said the fund would continue its work “in line with our mandate,” a statement from her office said. The Conspiracy of Fire Nuclei has claimed responsibility for the explosive device, also sent from Greece, that was discovered by the police at the offices of German Finance Minister Wolfgang Schaeuble.
The package was discovered on Wednesday, a day before Schaeuble was due to host his new US counterpart, Steven Mnuchin.
The outfit did not comment on the IMF hit.
Many Greeks blame Germany and the IMF for imposing years of public-sector cuts and policy overhauls in exchange for bailout packages needed to prop up the debt-ridden country. The group, which is considered a terror organization by Washington, sent mail bombs to foreign embassies in Greece and to European leaders in 2010...