Rice discussed developments in the region, including Palestine, Lebanon and Iraq.
A Saudi official said Iran’s nuclear programme was also discussed, with the issue set to dominate Rice’s tour.
Another Saudi source said Riyadh “considers it necessary to continue the dialogue with a view to a peaceful agreement” over Iran’s nuclear ambitions, which he said was also of concern to other Arab countries in the region.
She is to hold a news conference with al-Faisal on Tuesday morning before heading to Egypt.
She is also to visit Israel and the occupied Palestinian territories as part of the trip.
Iraq and Lebanon
On the aircraft to Jedda, Rice had said she intended to hold talks with King Abdullah about ways to help Mahmoud Abbas, the Palestinian president, and Fuad Siniora, the Lebanese prime minister.
During the flight Rice said: “I want Saudi’s involvement in the stabilisation of Iraq, I want Saudi’s involvement in the stabilisation of Lebanon, through resources and political support.”
Riyadh had a role to play in Iraq as it had contacts with a certain number of forces in the country, said the US secretary of state.
Saudi Arabia has also offered $1.5 billion to the effort to rebuild Lebanon after the July-August conflict between Israel and Hezbollah.
“Saudi Arabia has a lot of standing with a number of the forces in Iraq and they’ve actually been very helpful in trying to get Sunnis involved in the elections,” Rice added.
“I think it would be very helpful if they were supportive of and working toward helping Prime Minister [Nuri] Maliki’s national reconciliation plan, for instance.”