The accused, identified as Aman, made the 20-year-old girl hear gunshots by calling her on her phone and also called police to inform that he has shot dead the man.
His phone is switched off since then and he is on the run, a police official said.
The incident took place at around 2:30 AM when the alleged murderer called the victim identified as Owais Khan (32) out of his Bhajanpura house and following a heated argument took him to Jaffrabad at gunpoint, he said.
Around 4 AM, he rang up the 20-year-old girl and told her that he was going to kill her maternal uncle Khan.
"Despite repeated requests by the girl to spare his uncle, Aman shot Owais twice on his head and chest. He then called police and informed them about the incident and fled," the official added.
Owais Khan was taken to Guru Tegh Bahadur Hospital where doctors declared him brought dead.
Police said the victim's family did not inform them after his abduction and had they done that, a rescue effort could have been undertaken.
According to the victim's family, Aman is married and has a six-month-old daughter. But despite that, he had been teasing and harrasing the girl.
He had been pulled up by Khan over the issue several times in the past.
A case of murder has been registered against Aman and efforts are on to apprehend him, police said.