Rouhani blamed "extremist individuals" for the attacks, which targeted the Saudi embassy in Tehran and consulate in the northeastern city of Mashhad in response to Saudi Arabia's execution of prominent Shi'ite cleric Nimr al-Nimr.
He also condemned Saudi Arabia's execution of Nimr, calling it a violation of "human rights and Islamic values" and accusing the Sunni monarchy of pursuing "sectarian policies which have destabilized the region in recent years".
Demonstrators protesting Nimr's execution broke into the Saudi embassy building in Tehran earlier on Sunday, smashed furniture and started fires before being ejected by police.