The lower house of the country's Congress has voted to allow abortion in the first 14 weeks of pregnancy. President Macri has said if the Senate approves the bill, he will also sign it.
Lawmakers in Pope Francis' native Argentina on Thursday narrowly approved a bill to legalise abortion during the first 14 weeks of pregnancy.
Thousands of abortion rights activists cheered and hugged outside the Congress as the lower house Chamber of Deputies passed the bill by 129 votes to 125.
The bill will now go before the Senate, where it faces an uphill battle to become law. Analysts note that more senators have spoken out against the bill than in its favour.
TRT Wold's Monica Yanakiew has more.
The debate has divided Argentinian society. Though Argentina became the first Latin American country to legalise same-sex marriage in 2010, it remains strongly influenced by the Catholic Church and by the pope, who was formerly the archbishop of Buenos Aires.
"It's the time of women's rights," said Silvia Lospennato, a member of President Mauricio Macri's centre-right coalition.
Lawmakers wrangled through more than 22 hours of emotionally charged debate with nearly all 257 members having their say before the vote was taken, as activists on both sides of the abortion divide kept vigil in the streets outside.
When the result was announced, many anti-abortion protesters in the street hugged each other and wept — while abortion rights activists wildly cheered.
Mayra Mendoza, an MP for the centre-left Front for Victory Party, described the approval as "a debt of democracy."
Sebastian Bragagnolo, from the governing Cambiemos coalition, said "a woman is not entitled to an abortion, she has the right to health. The unborn child is biologically and scientifically a human being."
"Our women are out there; they're waiting for us; they're waiting for us to rise to the occasion," said Magdalena Sierra of the Front for Victory party, shortly before the vote was taken.
Luis Pastori, of the Radical Civic Union, said it was "absurd and unjust to sanction a law that enables the killing of human beings that must be respected from the moment of conception."
Many lawmakers have said they would put their religious convictions aside to support the bill.
The Church has campaigned fiercely against the new bill, and the pope sent a letter to Argentinian bishops calling on them to "defend life and justice."
As in most Latin American countries, abortion is illegal in Argentina, except in cases of rape or when the life or health of the woman is at risk.
The bill, if passed by the Senate, would decriminalise abortion during the first 14 weeks of pregnancy, and beyond that in cases where the fetus suffers from conditions not compatible with life outside the womb.
Argentina overcame strong Church opposition to legalise gay marriage eight years ago, but the issue of abortion has never before been discussed in parliament.
According to official health ministry statistics, more than 17 percent of the 245 recorded deaths of pregnant women and girls in 2016 were due to abortion. NGOs say some 500,000 clandestine abortions a year are carried out every year.
In Latin America, unrestricted abortion is legal in Uruguay, Cuba and Mexico City. In almost all countries, it is available in case of a risk to a woman's life or in cases of rape.
However, a blanket prohibition exists in the Central American states of El Salvador, Honduras and Nicaragua.