What authorities called "units specializing in locating and neutralizing perpetrators" were on the scene, police said in a statement.
"All of our emphasis at this moment in time is finding that suspect and all the different organizations -- security organizations here in Israel -- are working together to find that man," police spokesman Micky Rosenfeld told CNN.
Police have identified the suspect as Nasha'at Melhem, 31, an Arab-Israeli who lives in northern Israel.
Israeli authorities believe Melhem is the gunman who sprayed bullets from an automatic weapon near the Simta pub on Dizengoff Street in Tel Aviv, killing two and injuring at least eight before fleeing.
The man fired off more than 15 rounds in "a number of different directions," Rosenfeld said Friday.
An uncle of Melhem's told CNN that the man's father recognized Melhem in surveillance video of the attack broadcast by Israeli media, and immediately contacted police.
The uncle, Ahmed Melhem, gave the suspect's age as 29. He said the man has a psychological disorder and had been previously sentenced to five years in prison for attempting to steal an Israeli soldier's weapon.
"We are worried that a civilian in Tel Aviv might find him, and shoot him and kill him," Ahmed Melhem said. "Our second concern is that he might hurt himself. We urge him to turn himself in for his own safety."
The uncle said he did not know whether Melhem was taking medications he had been prescribed for the condition.
According to Melhem's uncle, the suspect's father works as a volunteer for Israeli police.
The father discovered after the attack that a weapon he kept in a safe at home was missing, the uncle said. It was not immediately known whether that was the weapon used in the attack.
Authorities have not confirmed the family's account.
More than 24 hours after the shooter was last seen, police continued to press the urgent search. Officers from several Israeli agencies set up roadblocks in Tel Aviv, checked homes and searched empty buildings around the city, Rosenfeld said.
"You have to understand the central area of Tel Aviv is a main populated area with hundreds of tourists that have come in for the new year, and we have to prevent any further incident from taking place," he said.
While authorities indicated they were only hunting for a single suspect, a statement suggested they were still open to the possibility that the man had help.
Among things police were looking at was whether the shooter was "a murderer who acted alone" in a criminal act or act of terror, authorities said.
Police are also attempting to determine if another incident in the Tel Aviv area was related to the attack on Dizengoff Street, Rosenfeld told CNN. He did not provide details of that incident.
Authorities asked the public to notify police of any suspicious activity.
Attack captured on surveillance video
The surveillance videos aired by Israeli news media appear to show the attacker before and during the 2:40 p.m. shooting, hours before Shabbat, Judaism's day of rest that starts on Friday evening.
In one video, the shooter can be seen putting a bag down on a shopping cart, pulling out what appears to be a gun, stepping out in the open and pointing the weapon.
As another person runs by, the shooter slide-steps to keep pace, still pointing the gun.
In the other video, the shooter is seen outside opening fire. In the foreground, in what appears to be an establishment's outdoor seating area, patrons hurry away.
Haim Pinto, owner of a jewelry store near the pub, said he was outside closing his shop when the shooting began.
"I saw people running shouting, 'Terrorist, terrorist!'" Pinto said in a telephone interview with CNN.
He said a shooter was "firing in every direction while he was running." Pinto said he went back into his shop, where he hid with two other people in a restroom.
"[It was] lucky that today was cold and wet, so that there were not too many people out," Pinto said. "Dizengoff Street on Friday is usually packed, and we are lucky that there was bad weather so there were not so many people."
Attack comes amid heightened tensions
The shooting came at a time of heightened unease in Israel and Palestinian territories, with a recent wave of violence that has included stabbings and other kinds of attacks on civilians and Israeli soldiers.
Nearly 1.75 million of Israel's 8.4 million residents are classified as Arab, according Israel's Central Bureau of Statistics.
Prime Minister Benjamin Netanyahu has called the spate of attacks, starting in October 2015, a "wave of terror." Twenty Israelis were killed from October to mid-November alone, with others injured, the government said.
Palestinian officials, meanwhile, have claimed Israeli authorities have repeatedly gone too far, saying that Israeli forces killed more than 80 Palestinians in the same period. The figure that includes protesters who died in clashes, as well as alleged attacks.