Former West Germany acknowledged the murder of six million Jews by the Nazis and began in 1952 to pay compensation eventually worth 3 billion marks (€1 .5 billion) to Israel. In 1992, two years after West and communist East Germany reunited, they agreed to provide further restitution.
The ministry said all Jewish victims of Nazi persecution who had not yet received any compensation were entitled to a one-off payment worth €2,556 ($3,300).
The ministry also said it would pay a lifelong monthly pension worth €300 to Jews who were interned in concentration camps or ghettos for three months or more or who had survived the Nazi regime by living in hiding or under a false identity for at least six months.
"In eastern Europe and the former Soviet Union there are still people who ... haven't been eligible to make a claim until this point. Now that we have identified such eligible claimants, it was decided that they also needed to be compensated," German Finance Minister Wolfgang Schaeuble said on Inforadio.
At an event in Berlin later where he signed the amended agreement, Schaeuble said: "When doing this work for the victims of persecution, everyone is conscious that we cannot undo the terrible events or the suffering and the injustice that was inflicted on millions of people and that no compensation or reparation can change anything about that."
He said the amended agreement meant that in eastern Europe a further 80,000 Jewish survivors of the Holocaust would be compensated and added that Germany would provide home care for about 100,000 Holocaust survivors around the world.
"The Shoah, the murder of millions, and the immense suffering that Germans caused German and other European Jews remains a part of our history," Schaeuble said at the event in Berlin's Jewish Museum.
"We have a duty and a responsibility to commemorate and remember but also to be vigilant against all forms of intolerance, xenophobia, anti-Semitism and racism," he added.
Jewish groups welcomed the decision as an important step.
"The Holocaust survivors are ageing and desperately need additional care and we're pleased that the German government responded to this additional need," said Deidre Berger, director of the American Jewish Committee's Berlin office.
"It's an important signal that despite the growing distance to the historical events, the German government continues to exhibit its responsibility to helping the survivors with their last years in dignified circumstances."
The Central Council of Jews in Germany said money alone would never make amends for the suffering experienced by survivors. "But through the compensation, victims get the recognition that is so sorely needed," said Council President Dieter Graumann.