The tension-filled delay came as German Finance Minister Wolfgang Schaeuble separately told reporters the only way Germany would let Greece remain in the eurozone and approve European Central Bank mass eurobond purchases would be if the European Union created a currency commissioner with sweeping powers to strike down national budgets.
European leaders are to hold a summit meeting on the eurozone crisis Thursday.
British newspaper The Guardian said the breakdown in Greece's talks with the European Commission, European Central Bank and International Monetary Fund -- known as the troika -- represented a new low in relations, despite efforts by both sides to put a positive spin on the talks.
Greek officials privately told the newspaper the troika had made "unreasonable" demands "at the 11th hour" that were not part of the deal when Athens signed up for its second $170 billion bailout agreement in March.
Many on the Greek side rejected the latest demands, which include drastic severance-pay cuts some negotiators said would return Greek labor conditions to "those of the Middle Ages," The Guardian said.
IMF Mission Chief Poul Thomsen told reporters late Tuesday both sides "agreed on most policy issues."
"On the few outstanding issues, we expect to cover them soon," he said.
Greek Finance Minister Yiannis Stournaras said "open issues" remained and Athens would make counterproposals soon.
"On the labor reforms issues, there was an initiative from the prime minister [Antonis Samaras] and in the coming days Labor Minister Yannis Vroutsis will propose solutions," he said.
By contrast, Democratic Left Party leader Fotis Kouvelis said: "The troika demands feed galloping recession. They exceed the endurance of Greek society."
Greek government officials say state coffers are expected to be empty next month and further rescue funding is crucial.
But the lenders insist Athens must agree to $18 billion in budget cuts in government spending, pensions and social benefits, as well as make structural reforms, if it wants to get the next $41 billion bailout installment.
Samaras was expected to explain the latest setback to other EU leaders when he attends Thursday's summit in Brussels, his first since assuming power in June, The Guardian said.
The summit is expected to pit Germany against the southern bloc after Schaeuble made his currency commissioner demands, British newspaper The Daily Telegraph reported.
Schaeuble said German Chancellor Angela Merkel agreed with the demands.
"When I put forward such proposals, you can take it as a given that the chancellor agrees," the Telegraph quoted him as telling German reporters.
One stunned EU diplomat told the Telegraph: "If that is the demand, they are not going to get it. Nobody in the [European] Council wants a new treaty right now."
The council is made up of EU heads of state and government.
Schaeuble said the currency chief should have powers similar to those of the EU's competition commissioner, who can approve or disapprove company mergers, state aid and anti-trust law throughout the 27-country intergovernmental union.