Greeted with a warm reception by Israel's prime minister, Vice President Dick Cheney said Monday that he looked forward to working toward Arab-Israeli "peace and reconciliation," despite 18 months of continual fighting between Israel and the Palestinians in the occupied territories.

Cheney said he was there to help build confidence between the two foes, and was anticipating a "land for peace" deal.

"Peace is not only possible, but necessary," Cheney said as the U.S. Special Envoy Gen. Anthony Zinni prepared meetings with a trilateral security authority of Israeli, Palestinian and U.S. negotiators.

Cheney was greeted by Israeli Prime Minister Ariel Sharon during a ceremony in front of the prime minister's office in Tel Aviv Monday with claims of unity in the war against terror.

Sharon, who shared a 45-minute car ride from the airport with Cheney and Zinni, greeted the vice president and said, "We stand with you in the war on terror." He added that Israel has always been fighting against terror.

Cheney said he was "delighted" to be back in Israel, a nation whose values are the same as those of the American people, and to meet with "his old friend" Sharon.

"Both Israelis and Palestinians have suffered mightily, and both deserve a better future. Both deserve to be able to send out their children without endangering them," Cheney said, referring to recent bombings at Israeli discos, pizzerias and shopping areas.

"I have in the past declared that in order to achieve a real, just and durable peace, I would be willing to make painful compromises," Sharon said. "But we cannot make any compromise on the security of our citizens and their right to live without the threat of terrorism and violence."

Cheney called on Palestinian leader Yasser Arafat "to live up to his commitment to renounce violence as a political weapon."

For the first time, Cheney referred to the Palestinian territories as "Palestine" during his trip, a term which Israelis still reject as long as peace eludes the Middle East.

Cheney was off to a Holocaust memorial before meeting with Sharon to discuss steps Israel can take to end the violence and "the devastating, economic hardship experienced by innocent Palestinian men, women, and children."

It is still undecided whether Cheney would meet with Arafat during his visit. A Palestinian official said no other person in the Palestinian leadership would meet with Cheney so it would be Arafat or no one at all.

Cheney said he will defer to Zinni, a retired Marine general, in matters on how he should handle any meeting with Arafat. Zinni, however, has been waging an uphill battle to push the Israelis and Palestinians toward a peace agreement. His job was complicated over the weekend by a suicide attack in Jerusalem and a fatal shooting north of Tel Aviv.

Cheney came to Israel from Kuwait, the final stop in a tour of nine Arab states. He carried a request from Arab leaders that he push the Israelis to allow Arafat to attend an Arab summit in Beirut, Lebanon, later this month.

Arafat has been under house arrest as the Israelis continue to confine him to his headquarters in the West Bank for as long as Palestinian militants continue to attack Israeli civilians. Sharon recently lifted some travel restrictions on the Palestinian leader, but he has yet to say if he will permit Arafat to travel to the Arab summit.

Fox News' James Rosen contributed to this report.