The bill passed the House of Representatives in a session lasting more than 20 hours.
It will now be sent to the Senate, and then to President Mauricio Macri, who has encouraged "responsible" debate over the topic and said that he personally opposes the legislation but will not veto it if Congress approves it.
The current law in Argentina prohibits abortion, except when the mother's life or health is determined to be in danger, or in cases of rape.
The bill passed Thursday, however, would allow abortion on demand up to the 14th week of gestation. Minors under 16 could get an abortion without having to inform their parents.
Health care workers under the bill could be eligible for conscience-based objections to participating in an abortion if they make such a request in advance "individually and in writing" to the director of their medical center. Institutions and health care facilities as a whole would not be allowed to conscientiously object to abortion.
Unidad Provida, (Pro-Life Unity), an Argentine NGO that serves as an umbrella group for some 100 pro-life organizations, called the House passage of the bill "lamentable," but assured that this outcome "does not intimidate us. It strengthens [our resolve]."