Saudi Arabia will face "divine revenge" over its execution of a top Shiite cleric, Iran's supreme leader Ayatollah Ali Khamenei said today after protesters attacked the kingdom's embassy in Tehran.

"The unjustly spilt blood of this martyr will have quick consequences," Khamenei told clerics in the capital, referring to Nimr al-Nimr who was executed along with 46 other men on Saturday.

"This scholar neither encouraged people into armed action nor secretly conspired for plots but the only thing he did was utter public criticism rising from his religious zeal."

Khamenei called the killing of Nimr "a political mistake by the Saudi government".

"God will not forgive... it will haunt the politicians of this regime," he added.

Angry crowds in Iran set fire to the Saudi embassy and consulate late Saturday night, with officials saying on Sunday that 40 people had since been arrested over the attack.

The strongest condemnation came from Riyadh's longtime rival Tehran.

"The Saudi government supports terrorist movements and extremists, but confronts domestic critics with oppression and execution," Iranian foreign ministry spokesman Hossein Jaber Ansari said.

It will "pay a high price for following these policies", he warned.

Saudi foreign ministry spokesman Mansur al-Turki called Iran's reaction "irresponsible", and Riyadh summoned Tehran's envoy in protest.

The demonstrators in Tehran hurled petrol bombs and stormed the Saudi embassy before being cleared out by police. Flames could be seen rising from the building.

"The fire has destroyed the interior of the embassy," an eyewitness told AFP, speaking on condition of anonymity.

Some of the "rogue elements" entering the embassy were arrested, Tehran police chief Hussein Sajedinia told ISNA news agency.

Riyadh said the executed men had been convicted of adopting the radical "takfiri" ideology, joining "terrorist organisations" and implementing various "criminal plots".