Kofi Annan met Israeli Prime Minister Ariel Sharon on Sunday and plans to travel to the West Bank on Monday for talks with Palestinian leader Mahmud Abbas and other top officials.
Stephane Dujarric, a spokesman for Annan, said the secretary-general hopes to help both sides "sustain the momentum that has been generated in the past few weeks".
The United Nations is one of the "Quartet" of sponsors of the road map, an internationally backed peace plan that stalled shortly after it was launched in mid-2003.
The plan called on Israel to freeze settlement activity in the West Bank and on the Palestinians to dismantle armed anti-Israel groups. Neither side delivered.
But a warming of relations between Israel and the Palestinians since the 11 November death of Yasir Arafat has raised hopes in the international community that the peace plan will soon be restarted.
"We want to see to it that the United Nations, as a member of the Quartet, sees to it that Israel's obligations from the road map are carried out," said Saib Uraiqat, the chief Palestinian peace negotiator.
We want to see to it that the United Nations, as a member of the Quartet, sees to it that Israel's obligations from the roadmap are carried out"
Saib Uraiqat, chief Palestinian peace negotiator
The United Nations' traditionally rocky relations with Israel are also likely to come up during Annan's trip. Israel has long accused the UN of being biased towards the Palestinians.
Israel's already troubled relations with the UN Relief and Works Agency - the main UN body serving Palestinian refugees - hit a low last year when Israel accused it of allowing Palestinian fighters to transport a rocket inside a UN ambulance. Israel later backed off the claims.
On the other hand, Annan has won praise in Israel for his tough stance on "terrorism", and the UN role in resolving a border dispute with Lebanon after Israel withdrew its forces from the country in 2000.
"Despite the sometimes difficult history between Israel and the United Nations, Kofi Annan has built up a level of trust and confidence with the Israeli leadership that I think previous secretary-generals have failed to do," said Mark Regev, spokesman for the Israeli Foreign Ministry.
He said that following Annan's recent decision to name a new UNRWA chief, Israel hopes it can "turn over the page" with the agency.
Annan is also expected to meet many of the 30 world leaders attending ceremonies on Tuesday and Wednesday for the inauguration of the new Holocaust museum at Jerusalem's Yad Vashem memorial.
"Despite the sometimes difficult history between Israel and the United Nations, Kofi Annan has built up a level of trust and confidence with the Israeli leadership that I think previous secretary-generals have failed to do"
Mark Regev, spokesman,
Israeli Foreign Ministry
The trip will take on personal significance for Annan.
His wife, Nane, is the niece of Raoul Wallenberg, a Swedish diplomat who saved tens of thousands of Jews during the second world war before disappearing.
Annan is expected to stop at the tree at Yad Vashem planted in honour of Wallenberg, whose fate was never discovered after his disappearance in Hungary on 17 January 1945.