U.S. Secretary of State John Kerry has repeatedly called leaders in Saudi Arabia and Iran to try to defuse their diplomatic row, U.S. officials say, according to BBC News.

State department spokesman John Kirby said the phone conversations involved foreign ministers of both countries and the Saudi deputy crown prince.

Saudi Arabia cut diplomatic ties with Iran on Sunday, January 3 after protesters ransacked the Saudi embassy in Tehran.

Protests erupted after Saudi Arabia executed a senior Shia Muslim cleric.

Sunni Muslim Saudi Arabia and Shia Iran are major rivals in the Middle East and back opposing sides in the conflicts in Syria and Yemen.

In his calls, Kerry stressed the importance of pushing forward on a peace deal for Syria, Kirby told a news conference.

"One of the key things on his mind is de-escalate the tensions, restore some sense of calm, encourage dialogue and engagement between these countries, but also to make the point there are other pressing issues in the region," Mr Kirby said. "Not letting the Vienna process [on Syrian peace talks] stall or fall backward is clearly top on his list," he said.