George Papandreou will resign as prime minister, and talks about the makeup of the new coalition government will continue Monday.
Papandreou had sought to build a coalition government in part to keep the European bailout of Greece in place, and in hopes of preserving its now tenuous position in the European Union.
The BBC reported that Papandreou agreed to resign in part because of the insistence of opposition parties that he not participate in any new coalition government.
Mr Papandreou narrowly won a confidence vote on Friday night, but had been under continuing pressure to resign amid chaos over the debt crisis.
A fresh bailout deal was agreed by the European Union last month, but Mr Papandreou faced the wrath of fellow EU leaders when he announced that he would put the deal to the people of Greece in a referendum.
The idea was dropped days later, but not without sparking a deeper financial crisis and triggering the political crisis which led to the confidence vote.
The bailout deal has still not been ratified by Greece, and the EU says no more funds will be released until it has been.
The bailout is big money. The EU would provide Greece with 130 billion Euro (about $178 billion) and would agree to let Greece write off half of its outstanding debts, in exchange for deeply unpopular cuts to social programs and government spending.
That program of austerity helped to drive resistance among Greek citizens, and is among the drivers of Papandreou's plunge in popular support.