The largest demonstration took place outside the congress in Buenos Aires, where the bill will begin debating next week.
This is the ninth time that a bill to legalize abortion has been presented in the strongly Catholic country.
In 2018, such a law was approved in the lower house but was voted down in the senate.
But this is the first time that the bill comes from the country's president - Alberto Fernández.
He has said that the new legislation would guarantee "that all women have the right to comprehensive care".
Current laws in Argentina allow abortion only in case of rape, if the mother's life is in danger or if the fetus is seriously injured.