Israeli Prime Minister Ariel Sharon (search) called Mahmoud Abbas (search) on Tuesday to congratulate him for winning the Palestinian presidential elections, the latest sign the two sides are eager to restart peace efforts after years of stalemate.

Since Abbas' landslide victory Sunday, Israel and the Palestinians have signaled their readiness to return to the negotiating table. The election and the formation of a new Israeli government that includes the dovish Labor Party have raised hopes around the world that talks might soon resume.

Tuesday's phone call, confirmed by Israeli and Palestinian officials, was the first direct contact between the two leaders since the election.

Sharon "congratulated him on his personal achievement and his victory in the elections and wished him luck," said a statement issued by the prime minister's office. "They agreed they would continue talking in the near future."

Earlier Tuesday, Sharon told his new Cabinet he hoped to meet Abbas in the "near future." He told the ministers the meeting would focus on security issues, especially efforts to "halt terrorism," according to participants.

Abbas is widely considered more moderate than his predecessor, Yasser Arafat (search), who died Nov. 11. Israel refused to negotiate with Arafat, accusing him of encouraging violence during the past four years of fighting between the two sides.

The last meeting between Israeli and Palestinian premiers was in August 2003, when Sharon met Abbas during his brief term as Palestinian prime minister.

Fresh from his victory, Abbas expressed hope late Monday that the sides will be able to return to the negotiating table.

"We extend our hands to our neighbors," Abbas said. "We are ready for peace, peace based on justice. We hope that their response will be positive."

Palestinian Prime Minister Ahmed Qureia (search) said plans for the meeting were still in an early stage.

"When the right time comes, we will go for a well-prepared meeting. We will not go just for a meeting, but for a useful one," he said.

In another development, Palestinian National Security Adviser Jibril Rajoub (search) resigned Tuesday. In a statement, he said he was giving a chance to Abbas to appoint his own adviser, leaving open the possibility he would return to the post.

Rajoub, one of the most powerful figures in the West Bank, was Arafat's security adviser for the last year of his reign.

After shunning Arafat for the last four years, Israeli officials have said they are eager to get to work with Abbas.

A senior Israeli Defense Ministry official said Tuesday that Israel was ready to hand over security duties in West Bank cities to the Palestinians.

The official, speaking on condition of anonymity, said discussions with the Palestinians on the issue likely would begin within days.

Israel has had security control over all West Bank cities since launching a large offensive in April 2002 in response to a suicide bombing that killed 29 people in the coastal city of Netanya. But it eased its military presence ahead of Sunday's election, raising the possibility of a more permanent pullback.

Israel has said progress in peacemaking will be linked to Abbas' ability to take on Palestinian militants.

The Hamas and Islamic Jihad militant groups have said they are ready to work with Abbas, but so far they have resisted his calls for a cease-fire.

Hamas militants fired several barrages of mortar rounds and homemade rockets at Israeli towns and Jewish settlements in Gaza on Tuesday. No one was wounded, but several buildings — including a synagogue packed with worshippers — were damaged.

An Israeli wounded Jan. 2 in a Palestinian rocket attack on the Erez crossing — the main Israel-Gaza border point — died of his injuries Tuesday.

Abbas has criticized militant attacks as damaging to the Palestinian cause. But he is reluctant to openly confront the militants, hoping instead to persuade them to accept a cease-fire.

Sharon, meanwhile, could face difficulties holding together his fragile coalition long enough to implement his plan to withdraw from the Gaza Strip and four West Bank settlements by year's end.

Sharon formed the coalition with the dovish Labor Party late Monday after narrowly winning a 58-56 vote in parliament.

Defense Minister Shaul Mofaz told the Cabinet on Tuesday that he expects the pullout, initially envisioned as a unilateral initiative, to be coordinated with the new Palestinian leadership. The pullout is scheduled to begin in July.

In the meantime, the Defense Ministry has asked Attorney General Meni Mazuz to review the legal implications of a plan to build a trench along a key patrol road on the Israel-Gaza border.

Defense officials, speaking on condition of anonymity, said digging the trench would require demolishing as many as 3,000 Palestinian homes in the border town of Rafah.

Military planners say the trench is the best way to prevent weapons smugglers from digging tunnels under the border. Militants have used tunnels to plant explosives under Israeli military installations.

Palestinian Cabinet minister Saeb Erekat condemned the idea, calling it "a catastrophe and a disaster for the Palestinian people."

The Israeli army has demolished hundreds of homes in Gaza in the past four years, saying the structures are used for cover by militants.

The Palestinians and human rights groups have condemned the practice, which has left thousands of Palestinians homeless.