The police had said in mid-August that they had found someone else’s DNA on Ms. Vetrano’s hands, throat and cellphone — the most promising early lead. But the samples they took did not match any stored in national databases containing profiles of known offenders.

Before long, her father called her cellphone, but she did not answer. He tried again and again. After two hours

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.

On Sunday, Mr. Vetrano said he would continue his campaign for familial searching.

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

The chief also said the attack “appears to be a chance encounter.”

Her mother, Cathie Vetrano, referred to the suspect as an “animal,” a “savage” and a “demon.”

Chief Boyce also said that Mr. Lewis made “detailed, incriminating statements” when detectives began questioning him.

Officials said the killing was apparently the brutal result of a random encounter. Chief Boyce said Mr. Lewis had no criminal record

The call came to detectives’ attention during a “deep dive” for additional clues

The police zeroed in on the man, identified as Chanel Lewis, in the last 10 days, after investigators reviewed a 911 call that placed him in the same part of the park in May.

20-year-old man