BRUSSELS — Fearing a renewed crisis in Greece that could set off economic shock waves, policy makers across three continents have scrambled to strike a deal to ease the country’s debt burden. There have been meetings in the United States, a diplomatic blitz in Europe and talks in Japan.

In an agreement announced early Wednesday, Greece won additional pledges of debt relief, but nothing substantial until 2018 at the earliest, and only then if it continues to carry out painful reforms. Even so, the accord could help ease concerns about another flare-up of a crisis in Greece as the region deals with a mass influx of migrants and a continuing terrorist threat.

Eurozone finance ministers also gave a green light for the next round of aid for Greece, money that would allow the country to pay bills in the coming months. Further final approvals for those disbursements will be needed, but ministers allocated 10.3 billion euros, or about $11.5 billion, for Greece, to be distributed in several stages starting with €7.5 billion as soon as the second half of June.

The plan for debt relief may also tamp down tensions ahead of the vote in Britain on June 23 over whether to leave the European Union.