BRUSSELS — European leaders said Monday morning that they had reached a deal meant to resolve Greece’s debt crisis and avert a historic fracture in the Continent’s common currency project.

“EuroSummit has unanimously reached agreement,” Donald Tusk, the president of the European Council, wrote on his Twitter account shortly before 9 a.m. on Monday. The new bailout for Greece would involve “serious reforms & financial support,” Mr. Tusk wrote.

The deal announced early Monday allows only the start of detailed negotiations on a new assistance package for Greece. But the prospect of a new bailout program was expected to give the European Central Bank the leeway to continue channeling sorely needed emergency funding to Greek banks hollowed out by capital controls and an economic slump.

The agreement, whose details have not yet been described, aims to provide Greece with its third bailout package in five years. Tough terms, demanded by Germany and others, are meant to balance Greece’s demands for a loan repayment system that will not keep it mired in recession and austerity budgets, against creditors’ insistence that loans worth tens of billions of euros would not be money wasted.

An accord would end five months of bitter negotiations that raised concerns that Greece would be the first country to be forced out of the euro currency union — a development that proponents of European unity had sought desperately to avoid.

“The advantages far outweigh the disadvantages,” Chancellor Angela Merkel of Germany told a news conference, explaining her decision to accept the deal and recommend that the German Parliament also grant its approval.

“The country which we help has shown a willingness and readiness to carry out reforms,” said Ms. Merkel, referring to Greece.

The total commitment of money has not been disclosed. But a document by the eurozone leaders noted that experts had estimated that Greece might need from 82 billion euros to €86 billion more — $91 billion to $96 billion — to shore up its economy, rebuild its banks and meet its debt obligations over the next three years. The document said Greece and its creditors should seek to “reduce that financing envelope,” if possible.

As part of Greece’s commitments, Ms. Merkel said, a fund will be created to use the proceeds from selling off Greek government-owned assets to help pay down the country’s debt. That fund would be “to the tune of” €50 billion she said.

Why a Greece Deal Matters

Greece will be required to also seek assistance from the International Monetary Fund and agree to let the organization continue to monitor the country’s adherence to its bailout commitments. The Greek government had resisted a continued role for the I.M.F., seeing the fund’s involvement as unwanted meddling.

The Greek Parliament will also be required to approve the terms of the agreement “without delay,’’ according to the document released Monday morning. One of the sticking points in the weekend negotiations had been a demand that the Parliament sign off on any deal by Wednesday, but that requirement appears to have been relaxed.

Mr. Tusk later used his Twitter account to write that steps would be pursued “to swiftly take forward the negotiations” on the latest bailout.

He added that eurozone finance ministers would “as a matter of urgency discuss how to help” Greece meet its short-term financing needs. That appeared to be a reference to ensuring that Greece, which is nearly bankrupt, can make large payments to lenders including the European Central Bank that are due in the coming weeks.

During the marathon negotiation session, Alexis Tsipras, the Greek prime minister, struggled with economic overhauls demanded by the creditors but which his left-wing government will find difficult to sell at home — just a week after Greek voters overwhelmingly rejected softer terms in a referendum.

European stocks rose and the bond market calmed on Monday morning just moments after European leaders said they had reached a deal to end the crisis in Greece, but there was no euphoria, as investors waited to see how the tough agreement would be put in place.