Iranian President Hassan Rouhani has placed a ban on American citizens to Iran in retaliation
Tehran called the ban, which includes green card holders, an “open affront against the Muslim world and the Iranian nation”.
Travellers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen have already been prohibited from boarding flights to the US after Mr Trump signed an executive order yesterday to pause entry for at least 90 days.
An Iranian Foreign Ministry statement, said: “While respecting the American people and distinguishing between them and the hostile policies of the U.S. government, Iran will implement the principle of reciprocity until the offensive U.S. limitations against Iranian nationals are lifted.
"The restrictions against travel by Muslims to America are an open affront against the Muslim world and the Iranian nation in particular and will be known as a great gift to extremists.”
The United States is home to an estimated one million Iranian-Americans.
Earlier on Saturday, Iranian President Hassan Rouhani said it was no time to build walls between nations and criticised steps towards cancelling world trade agreements, without naming Trump.
Mr Rouhani, a pragmatist elected in 2013, thawed Iran’s relations with world powers after years of confrontation and engineered the country’s 2015 deal which curbed its nuclear programme in exchange for relief from sanctions.
Other global leaders have warned Mr Trump against playing with the fragile relationship between America and Iran.
During a phone call with French President François Hollande today, he warned Mr Trump to be vigilant on Iran and said the nuclear deal should be respected.
Russian President Vladimir Putin also spoke to Mr Trump on the phone today, with the pair also discussing the Iranian nuclear programme as well as the situation on the Korean Peninsula.
Mr Trump’s most far-reaching action since taking office plunged America’s immigration system into chaos today, with not only refugees but legal US residents being turned away at airports as they feared being stranded outside the country.
Najeeb Haidari, a Yemini-American security manager in Yemen, said: "It's not right to portray huge groups of Arabs and Muslims as possible terrorists.
"This is a stupid, terrible decision which will hurt the American people more than us or anybody else, because it shows that this president can't manage people, politics or global relationships."
Immigration lawyers and advocates worked through the night on Friday trying to help stranded travellers find a way back home.
Lawyers in New York sued to block the order, saying many people have already been unlawfully detained, including an Iraqi who worked for the US Army in Iraq.
And Iranian film director Asghar Farhadi, is up for his second Oscar for best foreign language film at the Academy Awards with The Salesman but will not be able to attend the ceremony due to the ban.
Arab travellers in the Middle East and North Africa said the order was humiliating and discriminatory.
It drew widespread criticism from US Western allies including France and Germany, Arab-American groups and human rights organisations.