Maura Healey, who has signed other laws strengthening abortion rights. Under current Massachusetts law, abortion is legal for the first 24 weeks of pregnancy. Currently, 13 states are enforcing bans abortion at all stages of pregnancy, with some exceptions. Another four bar it after about six weeks of pregnancy — which is often before women realize they are pregnant. Most abortion-related state laws adopted this year have not made for major changes on when or how abortion is allowed.