Israeli Prime Minister Ehud Olmert has proposed holding a regional peace conference following the revival of an Arab peace initiative.
Olmert had hinted earlier at possible concessions for peace
Mr Olmert said if Saudi Arabia arranged a conference of "moderate" Arab states and invited him and Palestinian leader Mahmoud Abbas, he would attend.
Earlier, Mr Abbas urged Israel to engage in direct serious negotiations as soon as possible.
Last week Arab leaders urged Israel to accept a peace plan proposed in 2002.
Saudi Arabia has yet to respond but the BBC's Alim Maqbool in Jerusalem says Mr Olmert's call for a regional summit suggests the plan could at least form a basis for fresh negotiations.
SAUDI MIDDLE EAST PLAN
First adopted by Arab League in 2002
Calls for "full Israeli withdrawal from all the Arab territories occupied since June 1967"
Calls for Israel's "acceptance of an independent Palestinian State, with East Jerusalem as its capital"
All Arab states would establish "normal relations... with Israel" and "consider the Arab-Israeli conflict ended"
Calls for a "just solution to the Palestinian refugee problem"
The Saudi plan offers Israel normalisation of ties with Arab states if it pulls out of all Arab land it occupied in 1967 and agrees a "just solution" for Palestinian refugees.
Israel rejected the plan outright when it was first proposed.
But Mr Olmert said on Thursday Israel was ready to make "big and painful" concessions to advance the peace process.
Mr Olmert's call for a regional peace conference came during a news conference in Jerusalem with the visiting German leader, Angela Merkel.
"I am announcing to the heads of the Arab states on this occasion that if the Saudi king initiates a meeting of moderate Arab states and invites me and the head of the Palestinian Authority in order to present us the Saudi ideas, we will come to hear them and we will be glad to voice ours," Mr Olmert said.
"I think it is time to make a momentous effort in order to give a push to the diplomatic process... I am optimistic," he said.
"I invite all the heads of the Arab states, including of course the Saudi king whom I consider a very important leader, to hold talks with us," he said.
Correspondents say it is the first time Israel has called on Saudi Arabia - an important US ally which has no formal relations with Israel - to take the lead in peace negotiations.
Chief Palestinian negotiator Saeb Erekat said Mr Olmert should agree to the Arab peace initiative.
"I think if he accepts the Arab peace initiative, it would open the way to many conferences, not one," he said.
Mr Olmert did not specify which Arab countries he meant: they were taken to include Israel's "peace partners" Egypt and Jordan.