The proposal Tuesday by the Democratic Revolution Party, or PRD, the second-largest force in Congress, would allow women to have an abortion within the first three months of pregnancy. The bill also proposes that government health clinics provide women with abortions if they request them.
"We need to stop thousands of women from dying in unsafe operations," said Sen. Carlos Navarrete, who heads the PRD in the Senate. "This is a right our laws should guarantee."
Current Mexican law permits abortion only if the pregnancy endangers a woman's life or if the woman has been raped.
Many wealthier Mexican women travel to the United States for the procedures while thousands of poor women remain in Mexico and have back-street operations.
The PRD also has proposed legalizing abortion in the capital, where it holds the mayorship and a majority of lawmakers. Mexico City, with a population of 8.7 million, is a federal district similar to Washington, with its own legislature.
PRD lawmakers say that majority will guarantee that the capital becomes Mexico's first district to change the abortion rules.
But it could be harder to pass an abortion bill at a national level, where the conservative National Action Party of President Felipe Calderon holds a plurality in Congress, reports AP.
Calderon on Tuesday reiterated his position against abortion