JERUSALEM — An Israeli court convicted a 31-year-old man on Tuesday of abducting and murdering a Palestinian teenager in 2014, rejecting his late-hour insanity plea and bringing to a close a case that has convulsed Israelis and Palestinians.

The Jerusalem District Court ruled that the man, Yosef Haim Ben-David, had been fully responsible for his actions when he and two teenage nephews snatched Muhammad Abu Khdeir, 16, off a street near his East Jerusalem home, drove him to a forest on the outskirts of the city, choked him, beat him unconscious and burned him to death in the early hours of July 2, 2014.

Mr. Ben-David told investigators during a recorded re-enactment of the crime that he had urged his young relatives, who struggled with their captive in the back of the car, to “finish him off.” Prosecutors are demanding a life sentence.

One of the teenage defendants was sentenced in February to life in prison, and the other to 21 years, after the judges determined that he had played a lesser role in the murder. Their names have not been made public because they were 16 at the time of the crime.