George Bush, the US president, has dispatched Cheney to meet with Israeli and Palestinian leaders over the next two days to try to move forward rocky peace talks, despite recent violence.
At US brokered talks at Annapolis, Maryland, in November both Ehud Olmert, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, pledged to forge a peace deal by the end of this year when Bush leaves office.
However, there has been little visible progress because of ongoing violence and Israel's construction of new settlements on land which the Palestinians claim for a future state.
Israel is conducting peace negotiations with Abbas' West Bank-based government whilst fighting Hamas, which controls the Gaza Strip.
Scores of civilians were killed when Israel retaliated to rockets fired by Hamas into Israeli communities in southern Israel.
However, Egyptian efforts to broker a truce have created a recent lull in violence in Gaza.
In Jerusalem on Saturday, Cheney reaffirmed Washington's commitment to the establishment of a Palestinian state.
He assured Palestinian leaders that "they, too, can be certain of America's goodwill'' as it tries to help Israelis and Palestinians reach an accord.
"We want to see a resolution to the conflict, an end to the terrorism that has caused so much grief to Israelis, and a new beginning for the Palestinian people," Cheney said.
The vice president also said "we must not and will not ignore darkening shadows of the situation in Gaza, in Lebanon, in Syria and in Iran, and the forces there that are working to derail the hopes of the world."
Olmert said that he intends to speak to Cheney about Iran.
Israel considers Iran to be a security threat and rejects Tehran's claims that its nuclear programme is not designed to produce arms.
Olmert also said the two would discuss peacemaking and Hezbollah, the Lebanese group that fought Israel in 2006.
The White House has said Bush asked Cheney to visit Israel to discuss the peace process and other regional issues in advance of Bush's trip in May to mark the 60th anniversary of the modern state of Israel.