But expectations that the US-sponsored talks will result in a major breakthrough are slim.
 
Rice 'impressed'
 
At the news conference, Rice said she was "tremendously impressed by the seriousness" that Israeli and Palestinian leaders have shown in moving towards renewed peace talks.
 
She said: "I am quite confident that the will is there on both sides that people want to end this conflict."

In Jerusalem, Rice urged Israeli leaders to
be bold in pursuit of peace [Reuters]
Abbas said: "I agree with Prime Minister Ehud Olmert that there is a real possibility to achieve peace, and I say we are serious to use this opportunity to reach this historical peace."
 
He said he has received "encouraging signs" from Israel and the US, but expects tough going in the negotiations.
 
Abbas said Israel, the US and the Palestinians agreed that they should try to reach a peace deal before the end of George Bush's term in a year.
 
He called on Israel to begin immediately meeting its obligations under the first stage of the "road map" peace plan.
 
The plan requires Israel to freeze settlement construction, remove illegal settlement outposts and ease Palestinian movement.
 
Abbas said the Palestinians are ready to do their part, including trying to disarm Palestinian fighters.
 
Plea to Israel
 
Earlier in Israel, Rice urged Israel to "be bold" in pursuing peace with the Palestinians after Israeli leaders warned her there could be no deal on a Palestinian state until their own security was assured.
 
Hundreds of Israelis demonstrated against 
territorial concessions on Sunday [AFP]
In Jerusalem she Rice assured Ehud Olmert, the Israeli prime minister, that the US was committed to ensuring Israel's survival and said it was time to take "difficult decisions".
 
"It is time for us all to make difficult decisions for the sake of peace," she said in a speech to an audience that included Olmert on Sunday.
 
"All Israelis should be confident that America is fully behind you, that we are fully committed to your security and you can thus be bold in your pursuit of peace."
 
Olmert said he was ready to negotiate on all core issues after the initial conference despite raising questions over Palestinian leaders' ability to rein in armed groups.