U.S. Secretary of State Condoleezza Rice headed to Tel Aviv on Thursday on her latest push for Middle East peace, as Israel called for an extension of the Gaza truce despite an outbreak of violence.

During her visit to Israel and the West Bank, followed by trips to Jordan and Egypt, Rice will push for agreement on the outlines of Israeli-Palestinian peace before President George W. Bush hands over the U.S. presidency to Barack Obama on January 20.

Rice was scheduled to start her 19th visit in two years to the Middle East on Thursday afternoon, just one day after a fragile truce in and around the Gaza Strip was rocked by the worst violence since it went into effect in June.

Gaza militants on Wednesday fired a barrage of rockets and mortar rounds at southern Israel, without causing any casualties, after Israeli troops killed seven fighters in the besieged Palestinian territory.

Despite the violence, Israel said it hoped for an extension of the six-month truce reached through Egyptian-mediated indirect negotiations with Hamas, the Islamist rulers of Gaza who are listed as a terror group by the United States, the European Union and Israel.

"We hope the truce can again be applied, we believe in this truce and it looks like things are calming down," Deputy Defense Minister Matan Vilnai told Israeli army radio on Thursday.

The division of the Palestinian territories into a West Bank run by the U.S.-backed Palestinian Authority and a Gaza Strip run Hamas, which seized power violently there in June 2007, has hobbled the peace talks Rice helped revive after a seven-year hiatus at a conference last November.

Israel and the Palestinians pledged at the Annapolis, Maryland, conference to try and reach a deal by the time Bush leaves office, but little tangible progress has been made since then.

Chances of a swift breakthrough appear particularly slim as both the United States and Israel currently have "lame duck" governments.

Israeli Prime Minister Ehud Olmert, who resigned over a string of scandals, will remain at the head of a caretaker government until after February 10 elections.

Opposition leaders and even some of his cabinet members have said the current government lacks the powers to take part in negotiations.

Rice has nonetheless pledged to leave "no stone unturned" in her quest for a deal defining the contours of peace by January 20, when Obama moves into the White House.

She will hold talks with Olmert and Palestinian president Mahmud Abbas, as well as with Israeli Foreign Minister Tzipi Livni and right-wing opposition leader Benjamin Netanyahu, the leading candidates to become Israel’s new prime minister.

During her four-day trip to the region, she will also travel to the Egyptian resort of Sharm el-Sheikh for a meeting of the Middle East diplomatic Quartet -- the United States, Russia, the European Union and the United Nations.

On September 26, on the sidelines of the U.N. General Assembly in New York, the quartet members urged Israel and the Palestinians "to make every effort to conclude an agreement before the end of 2008" on all the core issues.

The borders of a future Palestinian state, the status of Jerusalem and the fate of 4.6 million Palestinian refugees and their descendents are at the heart of the negotiations.

The presence of more than 260,000 Jewish settlers in communities scattered across the West Bank is one of the main obstacles confronting the U.S.-backed peace process and continued construction in the settlements has drawn sharp criticism from the Palestinians and the international community.