The proposal was passed at a cabinet meeting despite strong opposition from the Roman Catholic Church, the conservative opposition Popular Party and even many supporters of Prime Minister Jose Luis Rodriguez Zapatero's Socialist Party.
The measure now will to go to parliament for approval, Deputy Prime Minister Maria Teresa Fernandez de la Vega told a news conference.
Under the proposed reforms, abortions would be allowed for women of 16 and over on demand up to the 14th week of pregnancy, and up to 22 weeks if there is a risk to the mother's health or if the foetus is deformed.
Women can also undergo the procedure after 22 weeks if the foetus has a serious or incurable illness.
"We want to offer minors as much protection as possible and the most respect for their basic rights," said de la Vega.
The existing law introduced in 1985, a decade after the death of right-wing dictator Francisco Franco, only allows abortion in cases of rape, fetal malformation and when a pregnant woman's mental or physical health is deemed to be at risk if the pregnancy goes to term.
The Popular Party has said it will challenge the reforms in the Constitutional Court, and the Spanish Family Forum, a coalition of Catholic groups, said it would stage a demonstration against abortion on October 17 in Madrid.
Popular Party spokeswoman Soraya Saenz de Santamaria condemned the reforms which she said "go against to the feelings of the vast majority of women and of parents."
An opinion poll carried out last June said 64 percent of people oppose the measure allowing 16-year-olds to have abortions without parental consent.
Among Socialist supporters, 56 percent said they opposed the move, according to the Metroscopia poll of 1,000 people carried out for the left-wing newspaper El Pais.
Zapatero has defended the changes, saying the state should not "intervene in the free and private decision of a woman, who is the one who has to take on the responsibility of a pregnancy during her entire life."
The prime minister has passed a series of sweeping social reforms since coming to power in 2004 that have angered the Roman Catholic Church.
He has pushed through legislation legalising gay marriage, allowing for fast-track divorces and giving increased rights to transsexuals, among other changes.