'Incitement to hate'
Mike Hamel, a gay rights activist whose organisation runs the youth club, said the centre was meant to be a safe place where gay teenagers, many of whom were still concealing their sexual identity from their families and friends, could meet with counsellors and other teenagers.
He blamed religious incitement against homosexuals for the attack.
"Beyond the pain, the frustration and the anger, we are facing a situation in which the incitement to hate creates an environment that allows this to happen," Hamel said.
Tel Aviv's mayor, Cabinet ministers, the country's chief rabbis and Prime Minister Binyamin Netanyahu condemned the attack.
"We'll bring him to justice and exercise the full extent of the law against him," Netanyahu said at the Israeli cabinet's weekly meeting.
Nitzan Horowitz, Israel's only openly gay lawmaker, called the attack a "hate crime".
"This is the worst attack ever against the gay community in Israel," he said.
"This act was a blind attack against innocent youths, and I expect the authorities to exercise all means in apprehending the shooter."
Micky Rosenfeld, a police spokesman, said the attack was "most likely a criminal attack and not a terror attack," while representatives of the gay community described it as "homophobic".
The report described the scene as a "bloodbath".
'All in shock'
Police have ordered the temporary closure of all gay clubs in the Israeli city.
Nitzan Horowitz, Israel's only openly gay member of parliament, condemned the shooting as a "hate crime".
He called it "without a doubt the biggest ever attack on the Israeli gay community".
"We are all in shock," he said.
Coastal, cosmopolitan Tel Aviv has a bustling gay scene, but open homosexuality is less welcome in conservative areas of Israel.
Annual gay pride parades in Jerusalem often turn violent with protests instigated by ultra-Orthodox Jews.