"This terrorist attack happened only a week after the meeting between the USA president (Donald Trump) and the (Saudi) backward leaders who support terrorists".
"We condemn these heinous attacks, wish Allah's mercy upon those who lost their lives and convey our condolences to the people of Iran, particularly to the relatives of those who lost their lives, as well as the Government of Iran, and wish a speedy recovery to the injured", the Turkish Foreign Ministry said in a statement.
If ISIS' claims are true, this would be the group's first major attack inside the Shia Muslim-majority country, which is one of the powers leading the fight against Islamic State militants in the region.
Jubeir said Saudi Arabia and other Gulf countries would be willing to reestablish normal ties with Iran if it changed its behaviour and stopped supporting militants and fighters in Lebanon, Yemen, Syria and elsewhere across the region.
The Sunni extremist group is at war with Iranian-backed groups in Syria and Iran and views Iran's Shiite majority as apostates deserving of death.
"In a prescheduled telephone conversation with Foreign Minister of Iran H.E. Dr. Mohammad Javad Zarif, External Affairs Minister Sushma Swaraj condemned today's terrorist attacks on institution of democracy and spirituality in Tehran". A semi-official news agency reported the siege had ended with four of the attackers killed.
Another lawmaker said one of the assailants was surrounded by security forces and all the doors to the building had been closed, ISNA news agency reported.
However, two senior government officials, who asked not to be named, said the attacks might prompt a blame game.
"Some coward terrorists infiltrated one of the buildings of parliament".
Speaker Ali Larijani dismissed the attacks, saying they were a "trivial matter".
Police officials later told the IRNA state news agency that they stopped another attacker from detonating a suicide belt in the parliament building.
ISIS has successfully attacked Iran, the United Kingdom, the Philippines and Iraq in the last week. Shops in the area were shuttered, and gunfire could be heard. It said a security guard was killed and that one of the attackers was killed by security guards. One eventually exploded a suicide vest while the others were killed by security forces.
The mausoleum is in southern Tehran, around 20 kilometres (12 miles) from the parliament building.
Pir Hossein Kolivand, Iran's emergency services chief, initially told the press at least 40 were wounded, a number that has since risen to 42 with 12 dead, according to Iranian state press as reported by the Independent.