President Trump said in the statement that while "we grieve and pray for the innocent victims of the terrorist attacks in Iran", nonetheless "we underscore that states that sponsor terrorism risk falling victim to the evil they promote".
Mohammad Javad Zarif wrote on his Twitter account: "Repugnant White House statement".
The Islamic State (IS) group, known as Daesh, its Arabic acronym, claimed the attacks, its first ever carried out in Iran.
The Law Enforcement forces in Kermanshah Province have arrested two people in Ravansar who are said to be involved in the terrorist attacks in the Iranian parliament and the mausoleum of Imam Khomeini, the late founder of the Islamic Republic.
They were the first attacks in Iran to have been claimed by the Islamic State group.
The five gunmen had returned to Iran in August 2016 for a terrorist operation under the command of Abu Aysheh, a ranking commander of Daesh, with the objective of carrying out attacks in Iran's religious cities, the statement said.
Several countries, including Germany, condemned the attacks in the Iranian capital, with Russian Federation saying it showed the need for greater worldwide cooperation to uproot terrorism.
Extra police were on the streets of Tehran on Thursday, a day after a pair of attacks targeted two iconic locations in Tehran.
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Saudi Foreign Minister Adel Al-Jubeir said he did not know who was responsible for the attacks and said there was no evidence Saudi extremists were involved.
According to Iran's intelligence ministry, five of the attackers had previously fought with the militant group in Raqqa and Mosul.
Iran's Supreme Leader Ayatollah Ali Khamenei said the attacks would have "no effect" on the country.
The United States and several allies in the Middle East have been fighting against the Islamic State. The reports said Iran's security forces neutralized one terrorist, another one committed suicide. Tensions are running high this week following a cut in ties between key Arab powers and Qatar over accusations that the energy-rich nation supports terrorist groups and is aligning itself too closely with Iran. The other said the attacks would push Iran toward "a harsher regional policy".
Last year Iranian authorities said they had foiled a plot by Sunni militants to bomb targets in Tehran and other cities during the Muslim holy month of Ramadan.
The attacks injured more than 40 people.
A separate terrorist group in the country has been detained before it managed to carry out any terror attacks.