Ms. Vetrano’s parents came down the steps of their tan-brick house at midafternoon to speak to reporters. Her mother, Cathie Vetrano, referred to the suspect as an “animal,” a “savage” and a “demon.”

Image Robert K. Boyce, center, the Police Department’s chief of detectives, arriving at the 106th Precinct station house in Ozone Park, Queens, to speak about the arrest in the case. Credit... Uli Seit for The New York Times

“Our sorrow is so endlessly painful that hearing the news is not what I expected,” Mrs. Vetrano said. “There’s no happiness.”

Chief Boyce said Mr. Lewis had received “a number of summonses in that area” dating to 2013. Those summonses, and the 911 call, apparently pointed detectives toward Mr. Lewis, who Chief Boyce said lives with his mother and is unemployed. The chief also said the attack “appears to be a chance encounter.”

Mr. Lewis now faces murder and sexual assault charges.

The case has remained unsolved into the winter despite appeals from the victim’s family and a reward that grew to more than $280,000. Ms. Vetrano’s father, Philip, and police investigators found her body just hours after she had gone for a run on Aug. 2 in Spring Creek Park.

It is a secluded park off Jamaica Bay where homeless people camp and teenagers roar by on all-terrain vehicles, even though A.T.V.s are prohibited in the park, part of the sprawling Gateway National Recreation Area. Ms. Vetrano was jogging on a fire trail, a pathway three miles long and just wide enough for a fire truck. She knew the route because she and her father had often jogged there, but she had gone alone that night because he had hurt his back.

Along the way, she exchanged text messages with a friend, but those messages stopped abruptly, the authorities said. Before long, her father called her cellphone, but she did not answer. He tried again and again. After two hours, he contacted a neighbor who is a police official, and officers were called in to search. Ms. Vetrano’s father joined them.