Under pressure from its creditors -- the European Union, European Central Bank and the International Monetary Fund -- the government agreed to adopt another 3.6 billion euros (USD 3.8 billion) in cuts in 2019 and 2020.
Athens conceded fresh pension and tax break cuts in return for permission to spend an equivalent sum on poverty relief measures.
The measures are to be approved by parliament by mid-May, with the government hoping to reach an overall deal at a May 22 meeting of eurozone finance ministers.
A general strike will be held against the cuts on May 17.
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A government source early today said Athens and the creditors were inching towards a preliminary agreement.
"There are four dossiers with important issues, and four or five dossiers with lesser issues (remaining)," the official said, according to state agency ANA.
In an interview Sunday, German Finance Minister Wolfgang Schaeuble said a May 22 deal was feasible "if the (Greek) government respects all the agreements."
Greece and its creditors agreed a third, 86-billion-euro (USD 94-billion) bailout deal in July 2015.
But the IMF has so far refused to take part after two prior programmes on the grounds that the targets were unrealistic and Athens' debt mountain unsustainable.
A compromise is required to unblock a tranche of loans Greece needs for debt repayments of seven billion euros in July.
Additional debt relief for Greece has proved a contentious point for many of its European creditors including Germany, where additional concessions are unpopular with a general election looming in September.