JERUSALEM — Four days after a gunman opened fire on a bar in the commercial heart of Tel Aviv, killing a manager of the bar and a customer, the suspect’s whereabouts and motives remained a mystery, and the authorities had apparently still not determined whether the shooting was an act of terrorism.

The suspect — identified by the police and relatives as Nashat Melhem, an Arab Israeli from northern Israel — fled the scene of the attack Friday afternoon. On Tuesday, he was believed to be armed and on the loose, sowing alarm among the Israeli public, particularly in the Tel Aviv area.

In a first public statement about the episode, Israel’s police chief, Roni Alsheich, appeared to confirm that the assailant had also fatally shot a taxi driver, Amin Shaaban, an Arab citizen of central Israel, apparently after getting into Shaaban’s cab along his escape route.

Shaaban’s body was found Friday afternoon in a sandy area along the Mediterranean coast just north of Tel Aviv, and his cab was found abandoned nearby.

The police said at the time that they were examining a possible link between Shaaban’s death and the shooting rampage that focused on the Simta bar on Dizengoff Street, a major commercial artery, and they have refused to release further details of the investigation. But during a condolence call on Tuesday at the home of one of the victims from the Simta bar, Alsheich conveyed condolences to other victims’ relatives and to the Shaaban family.

Hours after the assault, the minister of public security, Gilad Erdan, said it was unclear if the motive was political, terrorist, or criminal in nature. Since then, Prime Minister Benjamin Netanyahu and police officials have been careful to refer to the gunman as a murderer, rather than a terrorist.

Relatives of the suspect have described him as mentally disturbed. Questions about the case deepened Tuesday as the suspect’s father, Muhammad Melhem, a brother, and an aunt were held for questioning by the Israeli authorities. Another brother was released after being in detention for three days.

The Israeli news media said that the father was suspected, among other things, of being an accomplice to the crime and of interfering in the investigation.

The father, who volunteered with the Israeli police, has publicly condemned his son’s actions and told reporters during the weekend that he had alerted the Israeli authorities after it became clear from security-camera footage broadcast on television that his son was the gunman. On Monday, he appealed on Israeli television for his son to get in touch and turn himself in.

Nachmi Feinblatt, a lawyer for the father, told the Israeli news media that he had expected the authorities to detain the younger Melhem’s relatives for as long as he was at large — as a means of putting pressure on the fugitive and perhaps to glean information for the investigation.But Feinblatt said the “grave accusations’’ against the father were “light-years away from reality.’’

The search was focused in the last few days in the upscale neighborhood of Ramat Aviv in north Tel Aviv.