The proposal, which would expand abortion rights beyond current laws that allow the procedure only in cases of rape or when the mother's health is at risk, passed the lower house last month by 129 votes to 125.
Since then religious activists, particularly in rural parts of the country, have pushed back against the measure, which is backed by feminists and rights groups galvanized in recent years by efforts to stop violence against women.
The large crowds of supporters and opponents of the bill gathered outside, chanting, singing, praying and waving signs and banners.
The bill would make Argentina the third country in Latin American to broadly legalize abortion, after Uruguay and Cuba.
The bill, which would allow abortion through the first 14 weeks of pregnancy, may be amended by the Senate and sent back to the lower house.
The measure is supported by advocates who want an end to the unregulated abortions that, according to government data, are the country's leading cause of maternal mortality.
The proposal emphasizes the danger that poor women face in seeking the procedure under secret, illegal conditions.
When he opened the 2018 session of congress in March, Macri said that although he was against abortion, the time had come to debate the issue and that he would sign the bill if it were approved by Congress. Members of the leftist opposition, as well as Macri's conservative coalition, are divided on the issue.
Vice President Gabriela Michetti has come out against the bill, which languished for years in Congress before a strong women's rights lobby was forged during the national outcry over the 2015 murder of a 14-year-old girl.