An anonymous caller, saying he was from the Abd al-Aziz al-Rantisi unit of al-Aqsa Martyrs' Brigades, rang AFP in a northern West Bank town to claim the shooting.
Two other Israelis were wounded when the car in which they were travelling was attacked just outside Hebron.
Palestinian militant groups from across the political spectrum have vowed to avenge the killing of al-Rantisi in a 17 April Israeli air raid in Gaza City, as well as that of his predecessor Shaikh Ahmad Yasin in another raid one month earlier.
Earlier on Sunday, two Israelis were slightly injured in a mortar attack by Palestinians against a settlement on occupied land in the Gaza Strip.
The Israeli military said the rounds caused extensive damage to two houses, but failed to provide the name of the settlement.
One of many settlements on
occupied Palestinian land
The illegal settlement of Har Homa in east Jerusalem also came under automatic weapon fire from Bethlehem in the West Bank, but no one was injured.
Both attacks came as occupation forces arrested six Palestinians during a raid on Sunday morning in the West Bank town of Nablus, four of whom were on a wanted list.
Meanwhile, Israel's threat of physically harming Palestinian leader Yasir Arafat has come in for regional and international condemnation.
The resistance attacks came against the backdrop of more condemnation of a death threat made by Israeli PM Ariel Sharon against his Palestinian counterpart on Friday.
Egyptian Foreign Minister Ahmad Mahir said an attempt on Arafat's life would be a "crime that cannot be forgiven".
Israeli troops raided Nablus
"Whatever the Israeli government does, or however much it destroys or whoever it kills, it will not extinguish the Palestinian people who will continue to demand their full rights."
The secretary-general of the League of Arab States, Amr Musa, also warned against such a move and highlighted the long-term consequences of governments making violent threats.
Russia has added its voice to the condemnation of the Israeli PM's death threat against Arafat.
Foreign Ministry spokesman Alexander Yakovenko said Sharon's "threats against a legitimately elected head of the Palestinian Authority are unacceptable".
Sharon (L) told Bush he was no
longer bound not to harm Arafat
He noted Arafat had been recognised by the international community and urged Tel Aviv "to observe the norms of international law, including provisions of the 4th Vienna Convention".
The same criticism and opposition of Russia echoed in France, as the French Foreign Minister, Michel Barnier, called on Israel "not to initiate any action against President Arafat ... the elected and legitimate president of the Palestinian people".
But a deputy to Sharon said on Sunday there was no immediate plan to harm Palestinian Arafat despite the PM's renewed threats.
"Prime Minister Ariel Sharon does not intend to put something into action this very week, or today or tomorrow," Vice Prime Minister Ehud Olmert told Army Radio.
"He set out a position in principle regarding Arafat and the immunity he [Arafat] thought he enjoyed."
Sharon's death threat could rally support in his right wing Likud party before its 2 May vote on his plan to pull out from Gaza.