Differences also emerged among Greece’s lenders on how to make its debt sustainable into the next decade.
Greek PM Antonis Samaras has warned that without the new funds Greece will run out of money within days.
The ministers meeting in Brussels endorsed a proposal to extend from 2014 to 2016 a deadline for Greece to reduce its budget deficit, as demanded by international lenders.
The proposal was contained in a report for the ministers which also said the extension would add 32.6bn euros to the cost of the bailout.
Urgent bid for funds
The ministers will meet again on 20 November to discuss releasing the latest instalment of bailout funds.
The 31.5bn-euro tranche will first have to be approved by some national parliaments, including Germany’s.
Greece had been pushing for the funds after passing a tough budget for 2013, including further cuts to pensions and wages, in a vote on Sunday night.
More than 10,000 people joined demonstrations outside Greece’s parliament on Sunday to protest against the cuts.
However, the eurozone ministers said Greece needed to implement a “few remaining” prior actions to allow the bailout money to be released.
Greece faces a repayment deadline for 5bn euros of debt on Friday.
It is now expected to make an urgent bid to raise funds from the financial markets on Tuesday.
The draft document on the pace of Greek economic reform was prepared by the so-called “troika” – the International Monetary Fund, the European Central Bank and the European Commission. The text of the draft was published by the Financial Times website on Monday night.
The troika has already pledged 240bn euros in bailout loans to Greece.
The two-year extension in budget targets will give Greece time to achieve a primary budget surplus – a figure that would not include debt-financing costs.
The document says: “The smoother path will help to moderate the impact of fiscal adjustment on the economy.”
But the extension would cost an additional 32.6bn euros and comes with “very large” risks, the report says.
Those risks include the uncertain political support for the programme within Greece, the possible negative effect on the economy of the fiscal consolidation and possible court challenges to the measures.
Moreover, there is now an open difference of opinion between the eurozone and the IMF on how to make Greek debt sustainable in the longer term, the BBC’s Chris Morris in Brussels reports.
The chairman of the group of eurozone finance ministers, Jean-Claude Juncker, said the new target should be an overall debt level of 120% of GDP by 2022.
But the head of the IMF, Christine Lagarde, insisted that the target date should still be 2020 as originally envisaged.
It may seem like haggling over the details, but tens of billions of euros are at stake, our correspondent reports.
Under current policy, Greek debt will still be far higher by the end of the decade than anyone deems acceptable – meaning that new ways to reduce the debt stock even further are being discussed as a matter of urgency, he adds.