A bill passed its first stage in parliament, after two parties in the coalition government joined the opposition to vote in favour.
Last year, Israel's then-education minister endorsed the therapy, triggering a backlash.
The bill risks a political crisis, with religious parties unhappy at the move.
After the vote, the ultra-Orthodox United Torah Judaism (UTJ), which is part of the fragile national unity government, threatened to introduce bills which the centrist Blue and White - also a member of the government - would find objectionable.
The bill must still pass two more readings before it becomes law.
The term "conversion therapy" refers to any form of treatment or psychotherapy which aims to change a person's sexual orientation or to suppress a person's gender identity.
The practice is widely opposed on logical, ethical and moral grounds.
Earlier this week, UK PM Boris Johnson called the supposed method "absolutely abhorrent", saying that plans to ban it in the UK would be brought forward.
More about: Israel
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