The US Middle East envoy has arrived in the Saudi capital on the final leg of a regional tour aimed at reviving peace efforts, the Saudi official SPA news agency has reported.
George Mitchell met Prince Saud al-Faisal, the Saudi foreign minister, late on Saturday and was also expected to meet King Abdullah on Sunday.
The Saudi monarch is a key force behind the Arab peace initiative to resolve the Israel-Palestinian conflict.
Mitchell and Prince Saud discussed "the importance of moving the peace process forward" to achieve an independent, contiguous and viable Palestinian state, SPA said.
The US envoy has also visited Egypt, Jordan and Israel and held talks with Ehud Olmert, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president.
Amman talks
Earlier on Saturday, Jordan's King Abdullah II met Mitchell in Amman and urged Washington to resume its efforts to clinch a two-state settlement between Israel and the Palestinians.
King Abdullah II said after the meeting that he "insisted very serious negotiations should start on basis of a two-state solution as soon as possible."
"It's important not to lose time, and to move immediately to resume talks," Abdullah said, according to a statement issued by the royal palace.
The Jordanian king said the negotiations should be based on international agreements and incorporate the Arab peace initiative as the means to "ensure security for all in the region".
The peace plan, proposed by Saudi Arabia, offers Israel collective Arab recognition in exchange for withdrawal from territory it occupied in the 1967 war, the establishment of a Palestinian state with east Jerusalem as its capital, and a just solution to the Palestinian refugee problem.
Israel has said the initiative could be a starting point for discussion.