Washington has cautiously welcomed the rapprochement between the Saudis and anti-American Iran, despite the role of China, which it sees as its biggest global challenge.
Iran and Saudi Arabia compete for influence in Syria, Lebanon and Iraq.
They support rival sides in several conflict zones across the region, including Yemen, where the Houthi rebels are backed by Tehran and Riyadh leads a military coalition supporting the government.
In a separate development on Saturday, Omani mediators arrived in the Yemeni capital Sanaa to discuss a new ceasefire between the Iran-backed Houthi rebels and Saudi Arabia, an airport source said.
Diplomatic efforts to resolve the conflict have multiplied since the China-brokered Saudi-Iran deal to restore ties.