The outcome has embarrassed Antonio Guterres's ruling Socialists. It proves the country's conservative Catholic Church can have a powerful impact on government policy, reveals deep rifts between the Socialists themselves, and leaves the government in a constitutional tangle.
The negative result has also cast a shadow over a more controversial referendum, to be held in the autumn, on decentralising political power. The Church has been campaigning for months for a "no" vote, and anti-abortion priests have threatened to excommunicate those voting in favour. It was Church pressure that forced Mr Guterres to put the abortion law approved by parliament in February to the popular vote.
Mr Guterres's party pushed for a "yes" vote, but the Prime Minister himself, a devout Catholic, said it was a matter of individual conscience and that he personally would vote "no".
Critics on both left and right have condemned the poll's outcome. Alvaro Cunhal, the veteran Communist Party leader, said the referendum was unconstitutional because parliament had already decriminalised abortion in the first 10 weeks of pregnancy.
Why, the Communists asked, did the Socialists vote for a law in parliament - returning to the fray several times until they finally pushed it through - and then talk of individual conscience in a referendum?
Anibal Cavaco Silva, the Conservative former prime minister, said he was "seriously worried" by the high abstention rate, calling the whole exercise unnecessary. He believes the Portuguese people are happy with the 1984 law that permits abortions only in strictly defined circumstances.
Marcelo Rebelo de Sousa, leader of the centre-right Social Democrats, plans to block attempts to implement the law. "It would not be politically legitimate to go ahead," Mr Rebelo de Sousa said, a view echoed by the extreme-right Popular Party.
Mr Guterres is now torn over whether to defy the Church and press ahead with the law against his personal convictions, or drop it and thus undermine parliament.
Since 1984, abortions have been permitted if the foetus is malformed or if the mother's health is in danger. Only 300 legal abortions took place last year, but pro-choice campaigners put the tally of illegal abortions - punishable by up to three years' imprisonment - at up to 20,000. They say botched abortions are the main cause of maternal death in Portugal.Reuse content