US Secretary of State Colin Powell has urged Israeli and Palestinian leaders to make the most of new chances for peace in the Middle East.
Mr Powell called on the Palestinian leadership to tackle violence.
Mr Powell was visiting the region to stress US support for a smooth Palestinian election in January.
He said he was pleased with what both sides had told him about their willingness to co-operate on the poll.
Both sides must understand the need to end terror and the incitement to terror, he said.
Mr Powell said he wanted to reaffirm "President Bush's determination to take advantage of the opportunity that presented itself in the aftermath of Chairman Arafat's death".
Both the US and Israel accused Mr Arafat of undermining peace efforts and had refused to deal with him for some time.
Mr Powell's first stop on Monday was a meeting with the Israeli Prime Minister Ariel Sharon and the country's foreign minister, followed by a meeting with Palestinian leaders in the West Bank town of Jericho.
After their talks, Israeli Foreign Minister Silvan Shalom said Israel's first priority was the election of a Palestinian leadership "with whom we can sit down".
He pledged that Israel would "do everything in its power" to ensure the elections went ahead as planned.
Mr Powell has said he hoped his talks with both sides would help ensure the maximum number of Palestinians are able to vote in the poll on 9 January.
In Jericho, he met Mahmoud Abbas, who chairs the Palestine Liberation Organisation, Prime Minister Ahmed Qurei and acting President Rawhi Fattuh.
Palestinian officials said he had pledged to "stand shoulder to shoulder" with the Palestinians, and discussed freedom of movement for voters.
Mr Powell also stressed that the new leaders must tackle violence.
"What we really need is for the Palestinian side in this new era to speak out against terrorism," he said.
This is likely to be Mr Powell's final mission to the Middle East after announcing his resignation last week. National Security Adviser Condoleezza Rice has been named to replace him.
A US envoy, William Burns, met Palestinian leaders on Sunday - the first senior US diplomat to do so for months.
Arafat's death has brought a new reality to the region, says the BBC's Matthew Price in Jerusalem.
There is universal agreement that changes in the Palestinian leadership offer an opportunity for progress in resolving the intractable conflict, he added.
The crucial task will be to pressure both sides to ensure the forthcoming elections are peaceful.
But as Mr Powell flew in, there were reports of clashes in the West Bank town of Beitunia, west of Ramallah on Sunday.
Israeli troops shot dead three Palestinian men after they came under fire trying to arrest them in their car, the Israeli military said. One Israeli soldier was injured.
A local commander of a militant Palestinian group, the al-Aqsa Martyr's Brigades, was amongst the dead, said Palestinian sources.
Earlier, the Israeli army said an armed Palestinian was killed in the Gaza Strip after he was discovered in a building near the Jewish settlement of Gush Katif.