One bill would ban most abortions if a fetal heartbeat is detected. That can happen as early as six weeks into pregnancy.
A second bill would prevent women from having abortions based on gender selection or a genetic defect, such as Down syndrome.
The Republican-controlled Senate is expected to vote on both bills Friday, sending them to Republican Gov. Jack Dalrymple, who has indicated he would sign them.
Arkansas last week adopted a similar fetal-heartbeat bill at 12 weeks.
Abortion-rights advocates say a costly legal battle is certain if the North Dakota measures become law.