US Vice-President Dick Cheney has said peace between Israel and the Palestinians will require painful concessions on both sides.
Mr Cheney went straight into talks with Mahmoud Abbas
He said the creation of a Palestinian state was long overdue, but rocket attacks against Israel hindered peace.
Mr Cheney was speaking after talks with Palestinian President Mahmoud Abbas in the West Bank town of Ramallah as part of a Middle-East tour.
He has already given Israel strong backing on security issues.
The visit was part of a bid to revive the peace process, but correspondents say people on both sides remain sceptical.
It came as rival Palestinian groups signed a Yemeni-brokered reconciliation deal promising to revive direct talks - possibly next month.
Correspondents say it is the first real sign of progress since Hamas seized control of the Gaza Strip from Fatah last June.
Fatah wants Hamas to relinquish control of Gaza.
A leading Hamas official, Dr Moussa Abu Marzouk, told the BBC the aim of the dialogue was to restore all the Palestinian territories to a single control. But, he said, Hamas would retain control of Gaza until agreement was reached.
In Ramallah, Mr Cheney met Mr Abbas and Palestinian Prime Minister Salam Fayyad.
Mr Cheney said he looked forward to the day "that an independent, viable, democratic and peaceful Palestinian state comes into being".
"Achieving that vision will require tremendous effort at the negotiating table and painful concessions on both sides," he said.
"It will also require a determination to defeat those who are committed to violence and who refuse to accept the basic right of the other side to exist.
"A difficult but immutable truth must continue to be told: terror and rockets do not merely kill innocent civilians, they also kill legitimate hopes and aspirations of the Palestinian people."
Security was tight for the visit, with police blocking streets within several kilometres of the government compound.
Hamas spokesman Fawzi Barhoum said Mr Cheney's comments were "provocative and completely biased in favour of the Israeli occupation".
Earlier, Mr Cheney had reaffirmed US backing for Israel.
"America's commitment to Israel's security is enduring and unshakeable, as is our commitment to Israel's right to defend itself - always - against terrorism, rocket attacks and other threats from forces dedicated to Israel's destruction," he said at a meeting with Israeli Prime Minister Ehud Olmert on Saturday.
"The United States will never pressure Israel to take steps to threaten its security."
US President George W Bush has said he hopes for a peace deal before he leaves office in January.
But the BBC's Tim Franks in Jerusalem says Israelis and Palestinians are sceptical about the chances for peace.
Opinion polls suggest that most people doubt that the current talks, given an extra push by the Americans at the end of last year, will lead to a deal any time soon.
Mr Cheney is on the latest leg of a tour that has included Iraq, Afghanistan and Saudi Arabia.
Mr Cheney will visit Turkey before returning to Washington.