"As [US] President [George] Bush has said, the establishment of a state of Palestine is long overdue and the Palestinian people deserve it," Cheney said.
"Security and peace"
The visit to the Fatah-controlled West Bank is Cheney's first as vice president and is part of an effort to revive stalled peace talks between Israel and the Palestinians.
Cheney's visit to Ramallah, where he met Mahmoud Abbas, the Palestinian president, and Salam Fayyad, the prime minister, is the latest stop in his 10-day tour of the region.
Abbas, speaking at the same news conference, reiterated his call for Israel to halt settlement activities and military incursions into the occupied territories.
"Security and peace will not be realised with the continuation of the settlement activities and the establishment of roadblocks around cities and villages," the Palestinian president said.
Abbas also called for an end to "military escalations" in the Hamas-controlled Gaza Strip, from which his forces were routed in June, and demanded that Israel halt military incursions in the West Bank.
Cheney said that the establishment of a Palestinian state would require "painful concessions" from both Israel and the Palestinians.
But earlier, speaking in Israel, the vice president said Washington would avoid pressuring Israel to take steps that might threaten its security.
"America's commitment to Israel's security is enduring and unshakable, as is our commitment to Israel's right to defend itself always against terrorism, rocket attacks and other forces dedicated to Israel's destruction," Cheney said shortly after arriving in Jerusalem.
At US brokered talks at Annapolis, Maryland, in November both Ehud Olmert, the Israeli prime minister, and Abbas pledged to forge a peace deal by the end of this year when Bush leaves office.
But 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.
Scores of civilians were killed when Israel retaliated to rockets fired by Palestinian fighters into towns in southern Israel.
Egyptian efforts to broker a truce have created a recent lull in violence in Gaza.