Rice made the remarks in Riyadh on her tour of the Middle East that began in Saudi Arabia, Israel's Ha'aretz newspaper reported.
"Innocent Palestinians are caught in the crossfire and we call on all parties to stop," Rice said of last weekend's violent demonstrations. "The Palestinians deserve calm."
Rice said she was seeking to build support for Palestinian Authority Chairman Mahmoud Abbas and his Fatah party, locked in a power struggle with the Hamas party.
At a joint news conference with Rice, Saudi Foreign Minister Prince Saud al-Faisal said his government would not take a partisan stand, and said the region's many conflicts are rooted in the Palestinian-Israeli dispute.
"We think it is a core problem that, if settled, would have an effect on all the other core problems," Saud said.
Rice departed for Egypt for a meeting with President Hosni Mubarak and Foreign Minister Ahmed Abul Gheit as well as foreign ministers of eight Arab states.
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