Results today from 25 out of 26 cantons, or provinces, indicated 72% of voters were backing a proposal to allow abortions up to the 12th week of pregnancy, the news agency said.
The results showed 81% rejected a rival proposal to ban abortion completely. Final results were due in the evening.
Current Swiss law allows unborn children to be killed if the mother´s health is in danger. But no one has been prosecuted for undergoing or performing an abortion since 1988.
The government estimates between 12,000 and 13,000 abortions are carried out annually. Figures suggest one in nine pregnancies ends in abortion.
Under the new law, doctors and mothers still risk five years in jail if they break certain conditions, Reuters said. The law stipulates a woman seeking an abortion for psychological reasons must undergo an interview.
Ireland is the only European Union country where abortion is illegal. On the island state of Malta both abortion and divorce are illegal.
