Suspect in custody
Police said a man, named as Scott Roeder, 51, was being held in connection with one count of first-degree murder and two counts of aggravated assault.
Roeder had been detained about 270km away three hours after the shooting, police said.
Wichita police said they were investigating any ties Roeder may have had to anti-abortion groups.
Abortions can be considered late-term when performed after the 20th week of gestation when foetuses are potentially mature enough to survive outside the womb.
Mourners have gathered in Old Town in Wichita to commemorate Tiller.