Eyewitnesses are reporting that the fire seems to be located in the industrial area
Daesh, a militant group, claimed responsibility for both the attacks in the Shia majority nation, media reports said. Daesh posted a video showing what it claimed was footage from inside the high-rise Parliament building.
Iranian officials said they foiled a third attack.
It was not clear whether the death toll of 12 included the attackers or whether the victims were killed in both incidents or only at the Parliament, BBC reported. At least 40 people were injured, according to Emergency Services chief Pir Hossein Kolivand.
In the first incident, four gunmen armed with assault rifles forced their way into Parliament when it was in session and opened fire at security guards and visitors. Some reports said the terrorists entered through a public entrance, apparently dressed as women.
Iranian media reported that all four attackers were killed by the security forces. But by then damage had been done.
Iranian authorities denied there had been a hostage situation inside Parliament even as hundreds of security personnel, some in civilian clothes and armed with revolvers, ringed the building.
Speaker Ali Larijani downplayed the events, describing them as a "minor issue". But a lawmaker admitted that it was a major attack.
Minutes after the Parliament attack began, terrorists opened fire at the mausoleum of Khomeini, the founder of Islamic state of Iran.
The Governor of Tehran said one attacker detonated a suicide vest and another had been killed by security forces, state broadcaster IRIB reported.
Images from the scene showed grenades and magazines for automatic weapons, recovered from the body of an attacker. The suicide attacker was a woman.
Several visitors at the mausoleum were injured.
This was the most serious terrorist incident in Tehran since the early years of the Islamic revolution of 1979 led by Khomeini, the BBC reported.
Daesh has no following in Iran but has stepped up its Farsi language propaganda in a bid to woo the country's Sunni minority.
US condemns 'terrorist' attacks in Iran
"The depravity of terrorism has no place in a peaceful, civilized world," State Department spokeswoman Heather Nauert said.
"We express our condolences to the victims and their families, and send our thoughts and prayers to the people of Iran," the brief statement read.
The group said five Daesh fighters were involved in the attacks.
During a recent visit to Saudi Arabia, President Donald Trump blasted Iran as the "spearhead of terrorism."
Iran's Revolutionary Guards have vowed revenge for the attacks.
Eyewitnesses are reporting that the fire seems to be located in the industrial area
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