PHILADELPHIA (AP) -- The husband of a jogger found strangled in a park has been charged with her murder, police said Sunday, days after they warned female runners to take extra precautions until the killer was caught. Authorities announced the arrest of 48-year-old Christopher Murray at a Sunday afternoon news conference. His 46-year-old wife, Constance, was found dead Tuesday in Pennypack Park in northeast Philadelphia. The mother of two had been out running the night before. "The reality was he became a suspect early on and remained a suspect until he confessed," Lt. Philip Riehl said. Riehl said Murray has expressed remorse. "I think it was more of a rage incident more than premeditated," he said. Investigators say Murray trailed his wife in a car while she went out Monday night, and the two began to argue. Police say Murray continued to follow her, and the pair went to a bench at the park where they continued to fight. "She went up there voluntarily to talk to him about whatever was going on and things went bad," Riehl said. Christopher Murray strangled his wife and left her body near the bench, police said. He called police early Wednesday to report her missing, and a woman walking her dog found Connie Murray's body a few hours later. Surveillance video showed Christopher Murray in his vehicle, and he was taken in for questioning Saturday night, police said. Riehl said aspects of his story didn't add up. He failed a lie detector test and then confessed, Riehl said. Connie Murray's headphones and cellphone were recovered in a nearby sewer. A memorial service was scheduled for Sunday and the funeral for Monday, according to an obituary. The couple have two daughters, ages 12 and 15. In a phone interview with the Philadelphia Daily News last week, Christopher Murray described his wife's death as "devastating" and said she was "a beautiful woman, a loving, caring mother, a fabulous friend." Murray was denied bail, and no attorney is listed for him in court papers. A preliminary hearing is scheduled for Aug. 27.