"The actions last night by a group of radicals in Tehran and Mashhad leading to damage at the Saudi embassy and consulate are totally unjustifiable, as the buildings should be legally and religiously protected in the Islamic Republic of Iran," Hassan Rouhani said, quoted by the official IRNA news agency.
At least 44 people were arrested late yesterday for storming the diplomatic missions in Tehran and Mashhad after Saudi Arabia announced it had executed prominent Shiite cleric Nimr al-Nimr and 46 other men on "terrorism" charges.
But Rouhani criticised Saudi Arabia for killing Nimr.
"I have no doubt that the Saudi government has damaged its image, more than before, among the countries in the world -- in particular (among) Islamic countries -- by this un-Islamic act," he said in a statement.
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Yet, the people of Iran "will not allow rogue elements" to use the incident and "carry out illegal actions that damage the dignity of the Islamic republic establishment", he added.
Earlier today Iran's supreme leader, Ayatollah Ali Khamenei, said Saudi politicians would face "divine revenge" for their actions.