After meeting with Palestinian President Mahmoud Abbas, Cheney stressed the U.S. commitment to the creation of an independent Palestinian state, saying it was "long overdue."
"Achieving that vision will require tremendous effort at the negotiating table and painful concessions on both sides," said Cheney, whose stop in Ramallah came just two months after President Bush's trip to the West Bank.
"It also will require a determination to keep those who are committed to violence and who refuse to accept the basic right of the other side to exist," Cheney said.
Abbas, a moderate, controls the West Bank and is battling Hamas militants who have taken charge of the Gaza Strip from Abbas-allied forces and have bombarded southern Israel with rockets.
"Terror and violence do not merely kill innocent civilians, they also kill the legitimate hopes and aspirations of the Palestinian people," Cheney said.
In their meeting, Abbas asked Cheney to help stop Israeli settlement expansion and military operations targeting militants, said Saeb Erekat, an Abbas aide.
Speaking at the press conference, Abbas thanked Cheney for U.S. support. But he also lashed out at Israel's settlements and checkpoints. To reach peace, Abbas said, "what is required is will, courage and strong support from the international community, especially the U.S."
In his remarks, Cheney said, "A negotiated end to the Israeli-Palestinian conflict one that addresses the legitimate national claims of both people will have limitless value. Years of mistrust ad violence have achieved nothing, and the extremists who have stood in the way of a settlement have only caused further grief and suffering to the Palestinian and Israeli people."
"No one," he said, "deserves to go through live in a climate of fear of deprivation. ... That should not be and must not be the direction of events in this region."
Before the session, aides to Abbas said Abbas would tell Cheney there had been little progress in peace talks since the Palestinian leader and Israeli Prime Minister Ehud Olmert agreed to a resumption at a November conference hosted by President Bush in Maryland.
Cheney said "the future belongs to the advocates of peace and reconciliation." He cited Bush as saying that "the establishment of the state of Palestinian is long overdue." The Bush administration, Cheney said, will commit resources to help the Palestinians build the infrastructure necessary to prosper.
Cheney held talks with Israeli officials in Jerusalem before flying by helicopter to the West Bank. After seeing Abbas, Cheney planned a separate meeting with Palestinian Prime Minister Salam Fayyad.
The vice president began Easter Sunday with a prayer and the singing of "Amazing Grace" at a tiny chapel in Jerusalem, then launched into a day of talks about the Mideast peace process and the rising influence of Iran in the region.
"We are obviously dedicated to doing all we can as an administration to try to move the peace process forward, and obviously actively involved in dealing with the threats that we see emerging in the region not only threats to Israel, but threats to the United States as well," Cheney said in a meeting with Israel's president, Shimon Peres.
It was clear that Cheney was referring to Iran. Peres was more specific, saying the declarations that Iranian President Mahmoud Ahmadinejad makes against Israel cannot be ignored.
"We have this problem of the Iranians who want to build two satellites, the Hezbollah and the Hamas in Gaza. ... Nobody can control us and say that declarations by Ahmadinejad are less serious," Peres said. "We have to take it seriously."
He said time is of the essence in the peace negotiations, but that he believes progress is achievable.
Cheney is on a 10-day trip to the Mideast, where oil, the future of Iraq and Afghanistan and Iran's rising influence in the region have highlighted his talks with foreign leaders. His visit here is part of the Bush administration's strategy to keep the pressure on Israel and the Palestinians to reach a framework agreement for peace before Bush leaves office in January 2009.