Mitchell says it is critical to extend the Israeli-Hamas ceasefire
George Mitchell, the new US president's envoy to the Middle East, is to hold talks with Palestinian leaders amid continuing violence in the Gaza Strip.
He is due to meet Palestinian Authority President Mahmoud Abbas, but not members of Hamas which controls Gaza.
On Wednesday, he said it was vital to extend ceasefires declared after Israel's 22-day Gaza offensive.
Palestinian militants have now fired two rockets at Israel from Gaza and Israeli jets bombed a metal factory.
Mr Mitchell has said his visit, which comes less than a week into Barack Obama's presidency, showed the American commitment to peace.
Mr Mitchell has already visited Cairo during a week-long tour.
The US envoy has stressed Washington's commitment to pursuing a two-state solution in Israel and the Palestinian Territories.
But Palestinians are impatient to see talk translated into action after so many years of negotiations, says the BBC's Bethany Bell in Jerusalem.
They want to see the building of Israeli settlements in the West Bank halted, and an end to Israeli incursions in Gaza.
With the deep divisions among the Palestinian factions, Hamas and Fatah, still unresolved, and with an Israeli election looming, few in the region believe that change will come soon, our correspondent says.
Mr Mitchell's arrival in Israel came a day after Israeli forces clashed with Palestinian militants in the Gaza Strip.
US envoy George Mitchell: 'It is of critical importance that the ceasefire be extended'
After his meeting with Mr Olmert, the US envoy said: "The prime minister and I discussed the critical importance to consolidate the ceasefire including a cessation of hostilities, an end to smuggling and reopening of the crossings."
Late on Wednesday a rocket was fired from Gaza into southern Israel - the first since the ceasefire 10 days ago - hitting the Eshkol region in the western Negev without causing any reported injuries or structural damage.
Shortly afterwards, an Israeli jet pounded targets along Gaza's southern frontier with Egypt, hitting a metal factory in an area containing tunnels through which Israel says militants smuggle arms.
Another rocket was fired by militants early on Thursday, prompting correspondents to warn of a spiral of violence that could nullify each side's unilateral ceasefires that were announced on 17 and 18 January.
The US envoy began his trip in Egypt by meeting President Hosni Mubarak, who has been mediating between Israel and Hamas.
Mr Mitchell has not revealed the contents of his meetings in any detail, but has emphasised Washington's priority of creating a long-term ceasefire.
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