Greek Prime Minister Alexis Tsipras has warned of “real difficulties” ahead, as his government faces a Monday deadline to submit a list of reforms to lenders.
Under a deal agreed on Friday, the list must be approved by the international creditors in order for Greece to secure a four-month extension of its bailout.
“We won a battle, not the war,” Mr Tspiras said on Saturday.
The deal is widely regarded as a major climb down for the PM, who won power vowing to reverse budget cuts.
He hailed the agreement as a “decisive step” that “achieved much” towards ending austerity, but added: “We have a long and difficult road ahead.”
The BBC’s Mark Lowen in Athens says the government is engaged in a hard sell to the Greek people over the deal with eurozone ministers and the IMF in Brussels.
The Greek cabinet is discussing the potential list of reforms, which must be approved before eurozone members ratify the bailout extension on Tuesday.
Analysts say a collapse of the deal would revive fears of an exit from the euro, a so-called “grexit” – something both the EU and Greece say they want to avoid.
Mark Lowen, BBC News, Athens
After the late-night deal comes the hard sell to the Greek public. A government elected by promising to reverse austerity and end the bailout has had a major climb-down.
It has had to accept supervision by its creditors – no moves without EU agreement – and a loan programme with conditions.
To its voters, the government will stress that it now has a say in which reforms it is willing to make.
The hard-left of the party won’t like it, but the centre ground will, and Greece has staved off euro-exit for now. That is the success that the government will trumpet. But it is limited.
German Finance Minister Wolfgang Schaeuble stressed on Friday that there would be no payment of new funds to Greece until the conditions of the deal had been met.
Greek Finance Minister Yanis Varoufakis said he would work night and day until Monday to devise the list of reforms.
“If the list of reforms is not agreed, this agreement is dead,” he admitted.
Greece’s liberal daily Kathimerini warned on Saturday of “stifling” conditions attached to the deal in Brussels while the centre-left Ta Nea said both sides had made “compromises”.
The Greek Communist Party (KKE) accused the coalition, which is led by its far-left rivals Syriza, of extending the bailout without getting the loan conditions changed.
“Ultimately the bill will be footed by the people, as it happened with all previous governments,” KKE leader Dimitris Koutsoumbas said.
The government is already in trouble with its voters for seeking the bailout extension at all – something it swore it would never do.
On the streets of Athens, reaction to the deal in Brussels was mixed.
“I think it was positive in the sense that at least for now we can relax a bit,” one man, Nikos, told the BBC. “We will have to wait see what will happen next.”
But another man, Costas, dismissed the deal as a “somersault that the whole world will remember”.
Dutch Finance Minister Jeroen Dijsselbloem, head of the Eurogroup of eurozone finance ministers, said on Friday night that the deal was a “very important” step in the process of rebuilding trust between Greece and its creditors – the EU, the European Central Bank and the IMF.
Greek economy in numbers
Unemployment is at 25%, with youth unemployment almost 50% (corresponding eurozone averages: 11.4% and 23%)
Economy has shrunk by 25% since the start of the eurozone crisis
Country’s debt is 175% of GDP
Borrowed €240bn (£188bn) from the EU, the ECB and the IMF