Greece says it is hopeful it will receive the next instalment of its bailout loan from eurozone nations, after talks in Brussels.
However, the Eurogroup still wants Greece to create a privatisation fund and banking legislation before providing the cash.
It also says it will offer Greece a form of debt relief from 2018 if it completes reforms by then.
Greece agreed to a third bailout package worth €86bn (£60bn) last year.
On Sunday, the Greek parliament approved unpopular measures designed to overhaul tax and pension systems, a condition for receiving €5.4bn under the bailout deal.
Greece also has to specify how it would make further spending cuts if it fails to meet financial targets in the coming years.
Greek Finance Minister Euclid Tsakalotos was upbeat that a deal could be reached on the next tranche, after meeting fellow ministers in Belgium.
BBC economics correspondent Andrew Walker says some eurozone finance ministers, including the influential Wolfgang Schaeuble of Germany, also expressed optimism an agreement could be reached later this month.
Monday’s talks were focusing on debt relief measures aimed at avoiding the prospect of Greece defaulting in July. That is when Athens is due to make its next major repayment to the International Monetary Fund (IMF) and the European Central Bank.
The IMF believes Greece needs debt relief and says it will not sign off on a review of Greek reforms unless such relief is granted.
However, eurozone finance ministers say they have agreed to offer debt relief by giving Greece longer grace periods and bond maturities from 2018, if the country delivers by then on all reforms agreed under its latest bailout.
“This agreement on debt… by the European partners is expected to allow the IMF to participate in the programme,” the ministers said in a statement.
The IMF and other European partners are demanding Greece implement further austerity measures to generate an extra €4bn (£3.1bn) in savings – contingency money in case Greece misses future budget targets.
“A deal needs to address three issues: reforms – we are there – the contingency mechanism – we are almost there – and the debt issue – we are starting the discussion,” said European Commissioner for Economic Affairs, Pierre Moscovici, as he arrived for the Brussels talks.
The debate in Greece’s parliament on the reforms lasted for two days and protesters clashed with police in Athens in the lead up to the vote early on Monday.
Three days of a general strike also paralysed public transport and slowed the public sector.
Greek trade unions say the country cannot bear another round of austerity measures.