"I request Iran’s Interior Minister – with the cooperation of Judiciary and Intelligence Ministry – to identify the attackers and present them to judicial system so justice can be served," Rouhani said on Twitter.
The Iranian leader condemned the killing of Sheikh al-Nimr, warning it would only exacerbate terrorism in the region, but urged Iranians to refrain from retaliation.
"The Iranian people should not allow this to become an excuse for rogue individuals and groups to commit illegal acts and damage Iran's image," he stressed.
Sunni-Shiite tensions flared in the region in the wake of al-Nimr’s execution, with Shiites in Iran, Lebanon, and Iraq warning of repercussions.
Sheikh al-Nimr was an outspoken critic of the Saudi monarchy. He rose to prominence during the 2011 anti-government protests in the Sunni-dominated kingdom, where the Shiite population says they are being discriminated against.