LISBON, Portugal — Portugal’s prime minister said he will enact more liberal abortion laws in the conservative Roman Catholic country even though his proposal to relax restrictions failed to win complete endorsement in a referendum.

With nearly all the votes counted, almost 60% of voters approved the referendum allowing women to opt for abortions up to the 10th week of pregnancy, while slightly more than 40% opposed it.

However, under Portuguese law more than 50% of the country’s 8.9 million registered voters must participate in a referendum to make the ballot valid. The turnout Sunday was 44%.

Prime Minister Socrates, who is the leader of the center-left Socialist Party, said he would stick to his pre-ballot pledge to change the law through parliament where his party holds an overwhelming majority.

“Portugal will now tackle abortion in the same way as most other developed European countries,” Mr. Socrates said. Women seeking an abortion will first go through counseling “so that the decision is a considered one, not taken out of desperation,” he said.

It could still be some time, however, before the law is changed. A bill would have to be voted on first in parliament and then go to the president for approval. It would come into force only when the new legislation is published in the public records — a procedure that usually takes several months.

Debate over the abortion law, one of the most restrictive in the European Union, pitted the Socialist government against conservative parties and the Catholic Church, which claims more than 90% of Portuguese as followers.

Under current law, the procedure is allowed in the first 12 weeks of pregnancy if a mother’s health is at risk. In cases of rape it is permitted through the 16th week, and there is no time restriction if an abortion is the only way of saving a pregnant women’s life.

In most other EU nations, abortion is permitted within much broader limits. Women can ask for abortions up to the 24th week of pregnancy in Britain and up to the 12th week in Germany, France, and Italy.

Church officials made no immediate comment on the referendum.

Luis Marques Mendes, leader of the main opposition Social Democratic Party, said he would not stand in the way of granting broader abortion rights despite his opposition during the referendum campaign.

“Even though the [referendum] result is not binding, we believe it should be democratically respected,” he said.

Sunday’s low turnout confounded analysts. An editorial in the Diario de Noticias newspaper listed eight possible reasons for the high abstention rate, including the country’s conservative character, mistrust of politicians, and a reluctance to take a stand on such a hot-button issue.

It was the second time in less than 10 years that a referendum on the deeply divisive issue failed to draw enough voters in Portugal. In 1998, a majority of voters rejected a similar proposal; the referendum was declared void because of a low turnout, and Portugal’s policy remained unchanged.

An anti-abortion activist, Joao Paulo Malta, said the low turnout showed the majority had not spoken clearly and that voters remain divided.

Mr. Socrates, whose party took power in a landslide victory almost two years ago after he promised broad reforms and national modernization, described Portugal’s current law as “backward” and said it drives abortion underground.

Women seeking to terminate their pregnancies travel to EU countries where it is legal, especially to private clinics across the border in Spain where abortion is permitted on psychological grounds, or resort to shady, back-alley clinics at home.

Abortion-rights activists say about 10,000 women are hospitalized every year with complications arising from botched, illegal abortions.