MADRID—Spain's government is moving to curb abortion rights, keeping a 2-year-old election promise by a ruling party that has lost popularity during the country's recession and now seeks to shore up support among social conservatives.

A bill approved by the cabinet on Friday would rescind much of a 2010 law that made abortion widely legal before the 14th week of pregnancy. The reversal would buck a European trend toward easier access to abortion by allowing the practice only in cases of rape or a serious health risk to the mother, including psychological risk, or fetus.

Tens of thousands of people mobilized by women's rights groups and the main opposition parties took to the streets in 21 cities on Saturday to denounce the bill, many waving placards reading, "Abortion is not a crime."

The bill and the protests signal a return of social issues to the political agenda, which has recently been dominated by the economy, as Spain moves closer to elections.

Prime Minister Mariano Rajoy's government has made other recent nods to his Popular Party's conservative base. It is preparing a bill that would empower private security guards to detain criminal suspects, and it is also considering a measure that would reimpose life prison sentences for the first time in decades.