The discussion was initiated at the request of Israeli Arab legislator Issam Makhoul, a member of the left-wing Hadash Party. He recently appealed to Israel's Supreme Court to force the debate.
Rather than permitting the court to rule, Knesset Speaker Avraham Burg allowed the debate to go ahead.
At the start of Wednesday's Knesset session, about two dozen right-wing lawmakers walked out in protest.
The debate quickly turned into a shouting match between Arab and Jewish legislators. Five Israeli Arab lawmakers were expelled for heckling.
"The debate comes 40 years late," Makhoul said Wednesday. "It is also a sad day, for it reminds us that the Knesset shirked its role on the matter that threatens us with another Holocaust if we do no hasten to stop it before a disaster."
When Makhoul demanded that Israel go public with its nuclear program and eventually dismantle it, Cabinet Minister Haim Ramon, responding for the government, said Makhoul was hurting Israel's interests.
"Do you want us to tell Iran and Iraq exactly what we have and what we don't have? It's unheard of," said Ramon, who is minister in the Prime Minister's Office.
Instead, Ramon set out Israel's long-standing nuclear policy: that the Jewish state would not be the first to introduce such weapons and that Israel supports a Middle East free of nuclear weapons when there is no more risk of war in the region.
Makhoul requested the debate after Israel permitted excerpts from the trial of former nuclear technician Mordechai Vanunu to be published last November.
Vanunu has served 13 years of an 18-year sentence for disclosing Israel's nuclear weapons capabilities to the Sunday Times of London.