Israeli Prime Minister Ehud Olmert said on Tuesday that "real progress" had been made in talks with the Palestinians and "understandings and agreements have been reached on very important matters".

"The discussions we are conducting with the Palestinian Authority are serious and very significant," Olmert said on the eve of a visit to Israel by US President George W. Bush.

"We are making real progress and understandings and agreements have been reached on very important matters, although not on all of them."

Olmert said he hoped a comprehensive agreement could be reached with the Palestinians although he made no explicit mention of the January 2009 target date set by Bush.

"I hope an agreement between us will be reached, the realization of which will be gradual and in accordance with the roadmap," he said.

The latter was a reference to a five-year-old internationally drafted peace blueprint which sets out a phased path to peace starting with an Israeli commitment to halt settlement expansion in the occupied territories and a Palestinian commitment to improve security.

When the two sides relaunched formal peace negotiations at a US-hosted peace conference in November, they agreed to do so on the basis of the roadmap.

"This agreement will ensure the future of the state of Israel as a Jewish nation, with full American and international backing, and will be an Israeli-Palestinian agreement which will also receive the blessing of the Arab world," Olmert added.

The Israeli premier identified the biggest challenge ahead in the peace negotiations as the future borders of the Jewish state.

"I am convinced that the greatest and most important challenge we face today in the State of Israel, and according to which the future will be set, is the challenge of determining the permanent borders of the state of Israel in the framework of peace accords with our neighbours, which will be recognized by the entire international community," he said.

"I have often said in the past that we must strive to achieve an agreed-upon separation between the two peoples who live in the Land of Israel (Biblical Israel -- historic Palestine), based on two nations -- a Jewish nation and a Palestinian nation, living side-by-side in peace, security and good relations."

The Israeli government has made clear that it wants to retain sovereignty over major Jewish settlement blocs in the occupied West Bank, including annexed Arab east Jerusalem, under any peace deal.

Olmert said that Israel was also keen to forge ahead with peace deals with neighbouring Arab states. So far only Egypt and Jordan have signed peace treaties with Israel.

"Achieving peace agreements with other Arab countries is also very important for our future," he said.

"It goes without saying that in order to open a promising horizon for Israel's tomorrow, we must make every effort to moderate, and later on to dismantle and remove the serious security threats which darken our skies."

Peace negotiations with Syria have been frozen for the past seven years after Israrel baulked at Damscus's demands for the return of the whole of the strategic Golan Heights right down to the shores of the Sea of Galilee -- Israel's main water source.

But Israeli government spokesman Mark Regev revealed earlier this month that "preliminary work" had been carried out on resuming the talks.

"We don't just want to restart only a process of negotiations, we want to start a political dialogue," he told reporters.