Senators approved the so-called "abortion reversal" legislation on Friday. The House approved the measure in January.
GOP Gov. Doug Burgum has not indicated whether he would sign or veto the measure.
Supporters say doctors can give a woman the hormone progesterone to stop an abortion after she has taken the first of two medications needed to complete the abortion.
The American Congress of Obstetricians and Gynecologists says there is no medically accepted evidence that a drug-induced abortion can be interrupted.
North Dakota's proposal follows similar and successful bills in Idaho, Utah, South Dakota and Arkansas.