The previous Socialist government made abortion before the 14th week of pregnancy widely legal. But the ruling Popular Party has long sided with the Catholic Church on moral and social issues and made changing the law one of its main promises in the 2011 vote that brought it to power. The law needs parliamentary approval, where the Popular Party has a large majority.
"I am fighting for the rights of our children because I am 60 years old already and this no longer affects me directly," protester Pilar Rubio said.
Cristina Bermejo, 31, said she felt the introduction of the new law would set Spanish society back 40 years.
"In the rest of Europe, where previously many viewed us as an example of freedom and civil rights, now, they are questioning us, asking what on earth we are doing," Bermejo said.
A separate protest against Spain's new abortion law also took place near the Eiffel Tower in Paris. Among the protesters was Anne Hidalgo, Socialist candidate for mayor, and Inna Shevchenko, of the Ukrainian branch of the feminist group Femen.