It is a bid to encourage co-existence even in the most difficult times, with a wave of violence and unrest since the start of the month having raised fears of a full-scale Palestinian uprising.
Many Palestinians, Israeli Arabs and Israeli Jews weary from violence would likely look upon the effort with a great deal of scepticism.
But Tzafrir said: "I heard and saw many cruel and harsh things from both Arabs and Jews in these difficult circumstances, and I saw the stress and tension. But I believe that we must live together."
He said a number of groups had already taken advantage of the deal, but did not give a number.
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At least one other similar effort has occurred. In the old city of Acre in northern Israel, the owners of the Al Marsa restaurant, Moussa Alaa and Marwan Sawaed, invited the owners of nearby Jewish restaurants to join them for dinner.
"Acre is a mixed city, and the situation in the country affects the Arabs and Jews," Sawaed told AFP.
When violence starts, "the Arabs go with the Arabs and the Jews go with the Jews, and this affects Acre."
"We must live together for the solution. Sitting around a table eating and talking in a civilised manner is the best way to live a common life."
Arab Israelis make up around 17.5 percent of the population of Israel and are largely supportive of Palestinians in the occupied territories.
They are the descendants of Palestinians who remained after the creation of Israel in 1948, and they hold Israeli citizenship.