Tens of thousands of people took to the streets of Athens a day earlier to protest against the measures, imposed as a condition of $143bn bailout by the European Union and International Monetary Fund.
'Distress and outrage'
The protests turned violent when rioters smashed the windows of a bank in central Athens and hurled petrol bombs inside, setting the building on fire.
Firemen evacuated around 20 people from the wreckage of the Marfin Bank branch, where two men and a pregnant woman died of asphyxiation.
"I have difficulty in finding the words to express my distress and outrage," Papoulias said.
"Our country came to the brink of the abyss. It is our collective responsibility to ensure that we don't step over the edge. What is at stake in coming days is to keep social cohesion and social peace."
George Papandreaou, the Greek prime minister, branded the deaths as "murders", but defended the austerity measures.
"We are deeply shocked by the unjust death of these three people, our fellow citizens, who were victims of a murderous act," he said.
But he added: "We took these decisions [spending cuts] to save the country. The alternative would be bankruptcy."
Barnaby Phillips, Al Jazeera's correspondent in Athens said, a small minority had "hijacked the agenda" of the strike.
"It looked like a pitched battle for quite a while. An awful lot of tear gas used by the police, they would say no doubt to protect the parliament building and perhaps the people in it."
Estimates of the number of demonstrators varied from 27,000 to 100,000, making it the biggest protest since Greece was first hit by economic disaster late last year.
Al Jazeera's Phillips said that the government was likely to continue with its austerity programme, despite Wednesday's violence.
"Deaths like these are highly unusual. But I don't think the Socialist government feels that it has any choice ... it feels that Greece's debt crisis is such that it cannot back down," he said.
The cuts, some of which have already been implemented, will significantly affect civil servants' and pensioners' incomes.
Among the major measures announced on Sunday were a cut in bonus pay for civil servants and retirees; three years more for pension contributions; and the raising of the retirement age for women to 65, the same level as men.
The Socialists have an outright majority in parliament and so the measures are likely to be passed along party lines.