Mohammed Melhem was questioned on Tuesday along with five other family members and friends. They are suspected of being accessories to the killings on Friday.
The search for Nashat Melhem, 31, entered its fifth day on Tuesday.
On Monday, Mohammed Melhem made a televised appeal to his son to turn himself in.
“I call on my son directly, if you can, cooperate with me and contact me to arrange matters,” the elder Melhem said. “I will help you. Let’s end this saga. These are difficult days for the family.” He also condemned the attack.
Mohammed Melhem identified his son to police as the shooter in the hours after the attack after seeing his image on the surveillance footage taken during the attack. Two people were killed in the shooting.
On Tuesday, Israel Police said they believe that Nashat Melhem has escaped to northern Israel or the West Bank.
Chief Roni Alsheich said residents of Tel Aviv could “dramatically reduce the tension” without giving away any details of the investigation. He made the comments after visiting the family of Alon Bakal, one of the victims of Friday’s attack, to update them on the progress of the investigation.
“We are performing a search in collaboration with the Shin Bet security service, with many officers, and with special police forces,” Alsheich said. “Our primary goal is that it will be over quickly and without interruption. We are focused on one single mission – to catch the murderer.”
Thousands of police reportedly are involved in the search.