Isil has claimed responsibility for a co-ordinated attack by gunmen and suicide bombers on Iran's parliament and the shrine of Ayatollah Khomeini, the spiritual leader of the Iranian Revolution.
President Hassan Rouhani said the attacks in Tehran that killed at least 12 people yesterday would make Iran more united.
"Today's terrorist attacks in Tehran will make the Islamic Republic of Iran more determined in the fight against regional terrorism, extremism and violence," Mr Rouhani said in a statement published on the ISNA news agency.
"We will prove once again that we will crush the enemies' plots with more unity and more strength."
Teams of attackers struck the two sites in Tehran early yesterday morning, killing at least 12 and wounding dozens more, according to Iranian state media.
If confirmed that Isil was behind the attack, it would be its most ambitious operation yet against Iran.
One suicide bomber blew themselves up at the Khomeini shrine, which is highly symbolic for Iran's theocratic leadership. A second bomber later detonated explosives at the parliament during a stand off with security forces.
Isil's Amaq news agency released a short statement soon after the attacks, saying: "Fighters from the Islamic State attacked the shrine of Khomeini and the Iranian parliament building in the centre of Tehran."
The jihadist group claimed the credit with unusual speed and released a video of the attackers inside the parliament building.
Members of the Iranian forces took cover outside parliament.
Isil has recently stepped up its propaganda against Iran and in March released a video in Farsi, where it called on Iran's Sunni minority to rise up against the Iranian regime. The Sunni jihadist group considers Iran's Shia leaders to be apostates and worthy of death.