Two teams of attackers used gunfire and explosives to strike Iran's parliament and the mausoleum of Ayatollah Khomeini in Tehran Wednesday, according to state media.
Iranian media says several attackers, including suicide bombers, took part in the assaults on both sites, with the parliament attack still underway.
The IS group often claims attacks around the world, even when links to the group can not be confirmed.
Two senior government officials, who asked not to be named, said the blasts might prompt a blame game and exacerbate political in-fighting.
In the past few months, the group has upped its anti-Iran propaganda, and aimed to recruit from the country's Sunni minority community.
Pakistan has condemned twin attacks on Iran's parliament and a shrine to its revolutionary leader.
Mizan Online, an Iranian state-run news website, said 12 people were killed and 42 injured in the two attacks.
It was not immediately clear if the attacks were related.
It is now unclear how the attacker or attackers entered the parliament building, which is highly fortified, with multiple security checkpoints. If confirmed, these would be the first large-scale acts of violence claimed by ISIS in Iran.
Ten people remain in critical condition after London Bridge attack: Health Authority
The rampage was brought to an end when the trio were shot dead by armed police eight minutes after the first emergency call. Mr Thomas was last seen walking along London Bridge with his girlfriend Christine Delcros, who was seriously injured.
Ali Khalili of the Khomeini Mausoleum told IRNA that there were at least three, possibly four, attackers who opened fire on the tomb, and one of them detonated himself at the entrance.
Iran is deeply involved in the fight against ISIS, both in Iraq and Syria, and together with Russian Federation is a major backer of the regime of Syrian President Bashar al-Assad.
Iranian capital Tehran has been rocked by gun and suicide bomb attacks on the country's parliament and a shrine to former leader Ayatollah Khomeini.
In a message released by the Kremlin after Wednesday's attacks, Putin said Russian Federation "resolutely condemns" the violence.
Parliament was in session as the attacks unfolded and members were keen to show they were undeterred, continuing with regular business.
IRIB and Fars said an armed man was inside the mausoleum in southern Tehran, around 20km from the parliament building, with reports of several injuries.
At the parliament, or Majlis, four attackers reached the building's interior, where they shot at security guards. The country's powerful Revolutionary Guards vowed revenge and claimed the United States and Saudi Arabia were "involved".
"World public opinion, especially in Iran, sees the fact that this terrorist act was perpetrated soon after the meeting of the U.S. president with the heads of one of the reactionary regional states that has always supported ... terrorists as to be very meaningful", the statement read, according to the semi-official Fars news agency.
A video released by its news agency Amaq included an audio track of a man saying in Arabic: "Oh God, thank you".
Comments