LINCOLN, Neb. (AP) _ Gov. Ben Nelson signed a bill today that would require a parent to be notified in most cases before a girl 17 or under could have an abortion.

Nelson said signing the bill, which was passed by the Legislature on Tuesday, fulfilled a campaign promise to sign abortion legislation ''if I agreed with it.''

''Parental notification is an area I agree with,'' he said at a news conference.

The non-partisan, one-house Legislature passed the bill 32-12 after years of wrangling. In previous years the issue had prompted filibusters, but opponents said this year they were resigned that the measure would pass.

''We are grateful that parents will once again be involved in this very important decision,'' said Julie Lostroh of the Nebraska Coalition for Life.

But Susan Hale, a lobbyist for Planned Parenthood, said the state was ''interfering in the most private of family matters.''

Last year, the U.S. Supreme Court upheld state parental notification laws as long as the law provides a bypass procedure allowing a girl to seek court approval for an abortion if she does not want to tell a parent.

The Nebraska bill provides a such a bypass. It also waives the parental notification requirement if a girl's health was in immediate danger because of the pregnancy, or if the girl declared that she was a victim of abuse, sexual abuse or neglect. Abuse allegations would have to be made to the proper legal authorities.