The move paves the way for hearings on the bill followed by a public session for discussion and vote.
The draft comes as Israeli reprisal strikes on blockaded Gaza have killed more than 5,000 people in response to Hamas militants who killed at least 1,400 Israelis in a rampage after breaching the fence enclosing Gaza on 7 October.
"The draft law includes seven chapters, in which penalties reach life imprisonment sentence", Hela Jaballah, head of the freedoms Committee, said.
She added that normalisation, communication in trade, commercial and cultural activities, services, military or intelligence with Israel will be punished.
Tunisia does not have diplomatic ties with Israel, but Israeli tourists, most of whom are of Tunisian origin, take part annually in Jewish celebrations at Ghriba synagogue in Djerba.
This year, an attack near the Djerba synagogue killed two security officers and two Jewish visitors, one French Tunisian and the other Israeli Tunisian.
In recent years, Morocco, Bahrain, and the Emirates have normalised relations with Israel.
Saudi Arabia is putting US-backed plans to normalise ties with Israel on ice, two sources familiar with Riyadh's thinking said, signalling a review of its foreign policy priorities as war escalates between Israel and Palestinian group Hamas.
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