The execution was followed by an attack on the Saudi embassy in Tehran prompting Riyadh to sever ties.

"We're aware that the Kingdom of Saudi Arabia has ordered the closure of Iranian diplomatic missions in the kingdom" US State Department spokesman John Kirby said about the diplomatic rift.

"We believe that diplomatic engagement and direct conversations remain essential in working through differences and we will continue to urge leaders across the region to take affirmative steps to calm tensions."

The diplomatic fallout come as Iran's supreme leader said Saudi Arabia would face "divine revenge" for Saturday's execution of Sheikh Nimr al-Nimr and as Western nations voiced concern about escalating sectarian tensions between Sunnis and Shiite Muslims.

Nimr 56 was a force behind 2011 anti-government protests in oil-rich eastern Saudi Arabia.

He was put to death along with 46 other people Shiite activists and convicted Sunni militants who the Saudi interior ministry says were involved in Al-Qaeda attacks that killed dozens in 2003 and 2004.

After his execution a mob attacked the Saudi embassy in Tehran and a consulate in second city Mashhad.

Saudi authorities said they had asked their Iranian officials to ensure security at the embassy but Tehran failed to protect it.