The bill passed by the Legislature late Tuesday was aimed at keeping a late-term abortion provider from opening a clinic in the state, supporters of the law said.
The law passed short of the votes needed to prevent Parkinson, a Democrat and an abortion-rights supporter, from vetoing it.
Under the law, patients or their relatives could sue a doctor if they had evidence an abortion violated state law, The Wichita Eagle reported Wednesday.
Doctors would be required to provide a medical diagnosis to justify abortions performed after 21 weeks of pregnancy and involving fetuses considered viable.
The bill defined a viable fetus as one in which there was a "reasonable probability that the life of the child can be continued indefinitely outside the mother's womb with natural or artificial life-supportive measures."
Kansas has been without a late-term abortion provider since the killing last May of Dr. George Tiller by anti-abortion activist Scott Roeder, who was convicted of murder.