"The people spoke with a clear voice," said Socrates, whose Socialists have a majority in parliament.
"Our interest is to fight clandestine abortion and we have to produce a law that respects the result of the referendum."
Luis Marques Mendes, the leader of the main opposition Social Democratic Party, said he would not stand in the way of granting abortion rights up until the 10th week of pregnancy despite opposing it during campaigning.
"Even though the (referendum) result is not binding, we believe it should be democratically respected," he said.
Pro-abortion campaigners said they would continue to campaign until the law was passed.
Opposition to change was led by the influential Catholic church, which argued the government should do more to help women to have children instead of easing abortion restrictions.
One priest threatened Catholics who voted to ease the law with excommunication from the church.
The Bishop of the northern city of Braganca likened abortion to the execution of the former Iraqi leader, Saddam Hussein.
More than 90 per cent of Portugal's population identify themselves as being Roman Catholic although, as in other Catholic countries, regular church attendance is on the decline.
Portugal is one of a small group of European countries that also includes Malta, Ireland and Poland, in which abortions are banned.