Patricia Mercado, a feminist and former presidential candidate, said: "A woman can decide to have an abortion or not have it, but it's her decision.
"A secular state has the obligation to give the right to women to take this decision in the best conditions."
Mexico City is a federal district with its own legislature. The bill was proposed by the Democratic Revolution party (PRD) which holds a majority in the local assembly and party legislators are confident it will pass in April.
Abortion is legal in Mexico City in the case of rape and if a mother's life is threatened but, in the rest of the country, it is allowed only in the case of rape.
Assembly leaders argued that legalising the procedure will save lives, saying that 2,000 women die each year during illegal abortions.
Mercado said: "There are women who die today. We know there are four women every day [who die] because of bad abortions, especially poor women, and the state must respond to the problems of justice and public health that are brought on by clandestine abortions."
A PRD senator also sent a bill to the federal congress to legalise abortion nationwide, but the bill is unlikely to pass since Calderon's conservative National Action party has the largest voting bloc.
On Sunday, thousands of anti-abortion activists marched through the capital led by Cardinal Norberto Rivera, Mexico's most prominent cleric.
| NGOs say as many as 500,000 Mexican women|
undergo abortions every year [AFP]
Anti-abortion protesters argued that poor pregnant women need greater support.
Those protesters favour a bill they say would give poor pregnant women financial support, provide tax breaks for child rearing and give aid to adoption agencies.
The march followed an international anti-abortion conference featuring Cardinal Alfonso Trujillo, the Vatican's chief anti-abortion campaigner.
The Vatican does not want to lose its fight against abortion in Mexico, which has the second-largest Catholic population in the world. About 90 per cent of the country's 107 million people consider themselves Catholic and Calderon is an outspoken Catholic.
Mexico's constitution, however, bans religious groups from political activity and the PRD has called on the authorities to stop clerical involvement in the marches.