The vote is about putting into practice the tax hikes, pay cuts, privatisations and public sector redundancies approved in principle on Wednesday.
The vote was a retreat from the “grave scenario of default”, the EU said.
Public reaction has been very hostile, and the debate has been accompanied by strikes and violent protest.
Calm now appears to have returned and the BBC’s Malcolm Brabant in Athens says Athenian street-cleaning crews have come out in force removing debris from two days of battles in the square.
Debate starts at 0930 local time (0630 GMT)
Vote itself not before 1400
Roll-call vote with verbal response by MPs
Possible additional votes on individual articles
Government has a majority of eight over all other parties
Cabinet to meet after the vote
Some Athenians have accused the police of heavy-handed tactics, and newspapers have railed against what one called “an orgy of state terror”, our correspondent says.
Some accused the police of over-using tear gas.
Scores of people were treated for injuries and severe breathing problems.
MPs are not expected to vote before 1400 local time (1100 GMT), and it is not clear how many votes will need to be held to push the measures through.
All that has happened is that a default has been avoided at a moment when Europe’s banks are still vulnerable”
Government officials say they are confident that those who supported them in Wednesday’s vote, when the package was approved in principle by 155 votes to 138, would also vote for implementation, known as enabling legislation.
Its measures include:
The setting up of a privatisation agency
Preparation for privatisation of state-owned real estate
Curbs on public sector recruitment
Social security regulations
The opposition New Democracy party, which voted against the government on Wednesday, has said that it will support some elements of the bill involving privatisation and spending cuts.
“We will do what we can to support the government,” said MP Nikos Dendias, a former justice minister, quoted by Reuters news agency. “We will vote for two chapters of the bill today.”
Total Greek debt
An old drachma note and a euro note
Greece is about to get a second bail-out from the EU, aimed at helping pay its debts until 2014. It also has to agree more cuts as part of the deal.
Finance Minister Evangelos Venizelos has offered some concessions on tax, one of the most contentious parts of the package.
Some Socialist MPs have said they will vote against individual clauses such as an increase in heating oil levy and a rise in the minimum tax threshold.
The vote will enable Greece to receive the latest tranche of a 110bn-euro (£98bn) loan in time instead of defaulting.
But analysts say the real challenge will come after the loan is secured, and there is concern about whether the austerity measures can be effectively implemented in the face of so much public hostility.
Wednesday’s vote prompted a furious response from protesters in Athens.
Sporadic violent clashes were continuing in the capital in the early hours of Thursday between masked protesters – armed with stones and sticks – and riot police firing tear gas and stun grenades.
Despite the unrest, European Commission President Jose Manuel Barroso and European Council President Herman Van Rompuy welcomed the result as a “vote of national responsibility” paving the way for a second aid package.
June 29: Parliament approves new austerity package
June 30: MPs to vote on details of implementing package
July 3: EU will sign off latest bail-out payment to Greece – 12bn euros – if both votes are passed
July 15: Without the 12bn euros, Greece will default
Commentators: Does vote change anything?
The package of tax rises and budget cuts – worth about 28bn euros over five years – had been championed by Greek Prime Minister George Papandreou.
Had it been rejected, Greece could have run out of money within weeks. The EU and the International Monetary Fund have demanded that the measures are implemented before they extend further loans to Greece.
Greek unions are angry that the government’s austerity programme will impose taxes on those earning the minimum wage, following months of other cuts that have seen unemployment rise to more than 16%.
Once passed, European officials will start to finalise the details of a second bail-out, worth an estimated 120bn euros, designed to help Greece pay its debts until the end of 2014.