The New Year day shooting yesterday afternoon on Tel Aviv's busy Dizengoff street came amid a wave of Palestinian attacks on Israelis and days after the leader of the Islamic State (IS) group threatened the Jewish state with violence.
"Police are continuing to search for suspect who murdered 2 Israelis in central Tel Aviv," spokesman Micky Rosenfeld told AFP, adding that "road blocks were set up in different areas" of the coastal city.
Media reports identified the shooter as an Arab in his late 20s from northern Israel who had recently been jailed for attacking a soldier, but police refused to confirm.
Rosenfeld said there was a "strong possibility that this was a terrorist attack but we haven't ruled out criminal motives". He did not elaborate.
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CCTV footage from a nearby health food store showed a bespectacled young man with a backpack calmly pretending to shop before going to the exit, placing the backpack on a trolley, removing what looks like a submachine gun and opening fire in the street.
One of those killed was identified by his father as Alon Bakal, a law and business student who was a manager at Simta, the pub targeted, with police naming the second as Shimon Ruimi from southern Israel.
Police issued a gag order on the investigation as well as the one into the death of an Arab Israeli taxi driver found shot in north Tel Aviv a short while after the shooting rampage.
They have also refused to say whether the two incidents were linked.
Baghdadi said IS has "not forgotten Palestine for a single moment".
"And soon, soon with God's permission, you will hear the footsteps of the mujahedeen... We are getting closer to you day by day," he said.