Kuwait recalls ambassador from Tehran
The move comes following Riyadh's execution of prominent Shia cleric Nimr al-Nimr on Saturday, which sparked outrage in Iran.
Protesters in Tehran ransacked the Saudi embassy on Saturday, smashing windows and setting fire to buildings.
Saudi officials have said Riyadh will only restore diplomatic ties with Iran if Tehran gives up on ideas of expanding its regional influence.
"Iran [must] cease and desist from interfering in the internal affairs of other countries, including our own," said Saudi UN ambassador Abdallah al-Mouallimi on Monday.
"If they do so, we will of course have normal relations with Iran," Mouallimi added. "We are not natural-born enemies of Iran."
What's the beef? A brief history of Saudi-Iran relations |
International calls for restraint have urged Saudi Arabia and Iran not to further enflame tensions.
White House spokesman Josh Earnest expressed concerns about the situation, urging Saudi Arabia and Iran to show restraint.
The rupture in Saudi-Iran relations will likely hinder efforts to end Syria's five-year civil war, where Saudi and other Gulf states back rebel groups against Iran-backed Syrian President Bashar al-Assad.