Saudi Arabia will face "divine revenge" for its execution of a prominent Shia cleric, Iran's supreme leader Ayatollah Ali Khamenei has warned.

Ayatollah Khamenei described Sheikh Nimr al-Nimr as a "martyr" who acted peacefully.

Protesters stormed the Saudi embassy in Tehran late on Saturday, setting fire to the building before being driven back by police.

Sheikh Nimr was one of 47 people executed for terrorism offences.

But Ayatollah Khamenei said the cleric had been executed for his opposition to Saudi Arabia's Sunni rulers.

"This oppressed scholar had neither invited people to armed movement, nor was involved in covert plots," the ayatollah tweeted.

"The only act of #SheikhNimr was outspoken criticism," he added, saying the "unfairly-spilled blood of oppressed martyr #SheikhNimr will affect rapidly & Divine revenge will seize Saudi politicians".

Sheikh Nimr had been a figurehead in the anti-government protests that erupted in the wake of the Arab Spring up to his arrest in 2012.

Iran - Saudi Arabia's main regional rival - has led condemnation among Shia communities over the execution.