President Hassan Rouhani said the government is obliged to ensure the safety of foreign missions.
The president made the statement in the wake of the storming of Saudi Embassy in Tehran and its consulate in Mashhad by protestors enraged by the execution of Shia cleric Sheikh Nimr al-Nimr by Saudi Arabia.
"The move by some extremists in Tehran and Mashhad last night causing damage to Saudi Arabia's embassy and consulate, which, by Sharia and law, are supposed to be under the Islamic Republic of Iran's protection, is absolutely unjustifiable," Rouhani was quoted as saying by IRNA in a message on Sunday.
It is considered "a blow to the reputation of the Islamic Republic of Iran", he said, calling for a "decisive response" by the relevant authorities.
"The Interior Ministry is tasked with investigating the event resolutely in cooperation with the judiciary and the Intelligence Ministry to identify the attackers and bring them to justice."
Rouhani denounced the Saudi execution of the leading preacher as a "blatant breach of human rights and Islamic values".
"[The move] is in line with the same sectarian policies and terrorism and extremism in the region and the world, which have led to regional destabilization, war and conflict in recent years," he said.
Prior to the embassy incident, Deputy Foreign Minister for Arab and African Affairs Hossein Amir-Abdollahian called the Saudi charge d'affaires to the Foreign Ministry to hear Iran's protest.
"Riyadh is the main culprit behind the spread of terrorism in the region and cannot use diversionary tactics such as Sheikh Namir's execution under the pretext of fighting terrorism to justify its wrong policies that intensify insecurity in the region."
The Arab kingdom reacted to the remarks by summoning the Iranian ambassador.
Late on Saturday, a group of protesters stormed the Saudi Embassy in Tehran and set parts of the interior on fire before being cleared away by the police, ISNA reported.
Shortly afterwards, the Foreign Ministry issued a statement calling for calm and urging protesters to respect the diplomatic premises.
Hossein Jaber Ansari, the ministry's spokesperson, highlighted the government's commitments under international law to provide security for foreign embassies.
"The diplomatic police are duty-bound to deal with any violation of Saudi diplomatic premises … and will act to restore security to these premises," Ansari was quoted as saying by IRNA.
Tehran's police chief, Hossein Sajedinia, told ISNA that a number of "unruly elements" had been arrested for attacking the embassy.
Later, Tehran's Prosecutor Abbas Jafari Dolatabadi put the number of detainees at 40, saying, "Investigations are underway to identify other people involved in the incident."
The office of Tehran's governor general issued a statement on Sunday, banning any assembly outside the Saudi Embassy but authorizing a demonstration to be held at Tehran's Palestine Square upon the request of "some political groups".
