The U.S. State Department called on American citizens to "exercise increased caution" while traveling to Saudi Arabia, a travel advisory posted on its website said on Wednesday.
U.S. Mission personel and their families are not permitted to use the airport in Abha without Chief of Mission approval, the note added. Abha airport has been frequently attacked by drones and missiles launched from Yemen, where a Saudi-led coalition has been battling the Houthi group.
President Hassan Rouhani said on Wednesday Iran did not want conflict in the region while Defence Minister Amir Hatami said Tehran had no involvement in the attacks on Saudi Arabia's Aramco oil installations, media said.
Rouhani accused the United States and a Saudi-led military coalition of starting the four-year war in Yemen, according to Iranian news agencies.
"We don't want conflict in the region... Who started the conflict? Not the Yemenis. It was Saudi Arabia, the Emirates, America, certain European countries and the Zionist regime (Israel) which started the war in this region," Rouhani said in a video carried by Iran's media.
Rouhani says Iran-aligned Houthis attacked Saudi oil facilities at the weekend as a "warning", after attacks on hospitals, schools and markets in Yemen which have been blamed on the Saudi-led coalition.
"Rejecting comments about Iran's role in the operation, (Hatami) said the issue is very clear: there has been a conflict between two countries (Yemen and Saudi Arabia)," the semi-official Tasnim news agency said.