But critics complain the bill will cut pension and retirement payments as well as aid for some poor families.
On Monday, violent clashes erupted between police and protestors opposed to the measures near the country's congress building in Buenos Aires, with demonstrators continuing to bang pots and pans in protest late into the night.
Macri, in power since 2015, has been trying to limit pension payouts to lower the country's deficit, which is estimated at five percent of GDP.
But the opposition argues that the overhaul would negatively impact about 17 million retirees, as it would change the formula used to calculate benefits, adjusting payments quarterly while taking only the official inflation index into account.
"Voting is not the end of history," said Agustín Rossi, president of the Victory Front (FpV).
"What happened today is the starting point, the beginning of a peaceful resistance," Rossi said.
The crowd hurled objects including stones and bottles, trying to rip down metal barriers that police had erected to prevent them getting too close to the square beside Congress.
Last Thursday's session examining the bill was cut short after clashes escalated. Dozens of protestors and police officers have been injured in the skirmishes.
Some retirees who were protesting the measure were caught up in the middle of the violence when some demonstrators hauled rocks and gasoline bombs, and riot police responded with tear gas and rubber bullets. Others banged on pots in a traditional cacerolazo protest in several neighbourhoods of the capital late into the night.
The CGT umbrella union also called a 24-hour general strike that is grounding hundreds of flights. The measure was initially set to be debated on December 14, but the session was suspended because of violent clashes.