The Greek Foreign Ministry said Greece's ambassador to Germany submitted a formal request on Tuesday.
A parliamentary committee in 2016 estimated that Greece could claim minimum reparations of 292 billion euros ($328 billion) for World War II and an additional 9.2 billion euros for World War I.
A motion for the Greek government to act on the committee's findings received overwhelming support from lawmakers in April.
Germany has denied being obliged to pay reparations, saying the country's wartime debts were resolved long ago.
Pursuing the matter is popular with Greek citizens, and Greece has an early national election on July 7.