Mr Begin, the son of Menachim Begin, the patron saint of the Israeli right, was a candidate for the premiership but withdrew just before the polls opened. His newly formed National Unity party got only three Knesset seats in Monday's election.
It has been a bad week for Israel's far-right who were trounced at the polls. The main right-wing party, Likud, saw its leader Benjamin Netanyahu, the prime minister, defeated and its representation sink to its lowest level since the 1960s.
Pinhas Wallerstein, the leader of the Settlers' Council in the West Bank and Gaza, has also resigned, taking partial blame for toppling Mr Netanyahu's government last December and forcing an election. He said: "I cannot absolve myself of direct responsibility."
Ironically it was the far-right and the settlers who precipitated the fall of one of the more right-wing government's in Israel's history. They did so because Mr Netanyahu agreed last October, under US pressure, to a limited withdrawal from the West Bank at talks at the Wye Plantation in Maryland. He said he had made the minimum territorial concessions possible.
But the settlers hold that all of the West Bank was the land given by God to the Jews, and they were not prepared for compromise. Although Mr Netanyahu decided not to implement the Wye Agreement, the far-right and the settlers still brought him down. The result was an election in which the far-right was almost wiped out and the centre-left triumphed.Reuse content