Greek banks reopened on Monday and Athens paid debts due to the European Central Bank and International Monetary Fund.
Greek Prime Minister Alexis Tsipras faces his second major test in a week in parliament on Wednesday over reforms he wants lawmakers to adopt so bailout talks to keep the country in the euro can begin.
A first set of reforms that focused largely on tax hikes and budget reforms triggered a rebellion in his party last week and passed only thanks to votes from pro-EU opposition parties.
Tsipras is likely to need opposition votes again for measures parliament will vote late today on propping up failed banks and speeding up the justice system -- two more conditions to start talks on the 86 billion euro rescue deal.
The government hopes the negotiations can then start this week and be wrapped up by August 20, but with divisions within Tsipras' leftist Syriza party laid bare by the votes, snap elections are likely in the autumn.
"Tsipras' rupture with the Syriza rebels," center-right daily Ethnos said on its front page as most dailies focused on divisions in the party.
"Rendezvous in September," pro-Syriza Avgi newspaper wrote on its front page, saying a party congress was likely then, with elections lurking in the background.
In the first signs of a return to normality, Greek banks reopened on Monday and Athens paid debts due to the European Central Bank and International Monetary Fund.
On Tuesday, Standard & Poor's upgraded Greece's sovereign credit rating by two notches, saying the country's liquidity perspective has improved with bailout talks.
But the fresh austerity measures are hard to accept in a country whose economy has contracted by a quarter during five years of crisis and where unemployment is more than 25 per cent.
The main public sector union ADEDY has called for a rally on Wednesday evening in front of parliament.
"We will continue our battle so that the new barbaric bailout does not pass and is overturned," ADEDY said in a statement, urging Greeks to rally against "a neocolonial control" of the country by the EU and the IMF.
Anti-austerity rallies last week briefly turned violent when masked youths hurled petrol bombs at police as lawmakers were debating the first bailout bill.
Tsipras himself has said he disagrees with the measures demanded by Greece's euro zone peers and other international creditors for talks to proceed on a third bailout to save the country from bankruptcy.
But after he made a u-turn by accepting a deal at the 11th hour to keep his country in the euro, he told party hardliners on Tuesday they, too, should face reality.
"Up until today I've seen reactions, I've read heroic statements but I haven't heard any alternative proposal," he told Syriza officials on Tuesday, warning that party hardliners could not ignore the desire of most Greeks to stay in the euro.
"Syriza as a party must reflect society, must welcome the worries and expectations of tens of thousands of ordinary people who have pinned their hopes on it," he said, according to an official at the meeting.
Image: Greek Prime Minister Alexis Tsipras is seen on a television monitor while addressing the nation. Photograph: Reuters