ATHENS — European and global financial leaders agreed Tuesday to release $57 billion in critical loans to Greece and provide billions in additional debt relief in order to help the country stabilize its ailing economy.

After three weeks of negotiations, Greece’s euro partners and the International Monetary Fund agreed to release the loans in four installments beginning next month. The leaders also settled on a raft of measures — including a debt buyback program and an interest rate cut on loans — that will reduce the country’s debts by about $51.8 billion.