Iran's foreign ministry announced it will limit issuing visas to American tourists in retaliation against the immigration crackdown.
The official IRNA news agency carried a statement by the Iranian foreign ministry saying Iran will resort to "counteraction" to Mr Trump's executive order.
The statement said: "Iran, to defend the dignity of the great Iranian nation, will implement the principle of reciprocity until the removal of the insulting restriction against Iranian nationals."
The statement adds: "It will apply corresponding legal, consular and political actions."
The two countries have had no diplomatic relations since 1979 when militants stormed the US embassy.
A sweeping new travel ban introduced by Donald Trump is causing chaos and panic worldwide.
The president issued an executive order yesterday banning nationals of seven Muslim-majority countries for three months - banning those fleeing from war-torn Syria indefinitely - and stopping the admission of all refugees for four months.
The Executive Order has been implemented by US Customs at Dublin and Shannon airports, as well as at ports of entry across the United States.
A note on the US Embassy website says that nationals of the countries listed on the Executive Order who have already scheduled a visa interview in Dublin, should not attend their appointment, as the Embassy will not be able to proceed with the visa interview.
In the US, New York immigration lawyers have moved to block the order saying numerous people have already been detained and many others turned away while Google has urged around 100 employees to return as soon as possible from abroad, for fear they could be affected.
Debbie Almontaser, from the Muslim Community Network, said: "The impact of this executive order will be immense, on immigrants as well as Muslims.
"We fear that it will further marginalize communities "
Airlines have been forced to turn away passengers due to fly to the United States.
Dutch airline KLM says it has had to turn away seven would-be passengers.
Manel Vrijenhoek, at KLM's press office, said: "We would love to bring them there. That's not the problem. It's just that this is what the US sprang on the rest of the world - that these people are no longer welcome."
She said the seven were due to fly with KLM from different airports around the world. Ms Vrijenhoek confirmed they were from countries affected by the three-month immigration ban: Iraq, Syria, Iran, Sudan, Libya, Somalia and Yemen.
Qatar Airways is advising passengers bound for the US from banned countries that they need to have either a green card or diplomatic visa to travel.
A statement on the company's website says: "Nationals of the following countries: Sudan, Libya, Somalia, Syria, Iran, Iraq, Yemen ... may travel to the U.S. only if they are in possession of a permanent resident card (Green card) or any of the below visas."
Cairo airport officials said seven US-bound migrants - six from Iraq and one from Yemen - have been prevented from boarding an EgyptAir flight to New York's JFK airport.
The officials said the seven migrants, escorted by officials from the UN refugee agency, were stopped from boarding the plane after authorities at Cairo airport contacted their counterparts in JFK airport.
The Council on American-Islamic Relations said it would challenge the constitutionality of the executive order.
"There is no evidence that refugees - the most thoroughly vetted of all people entering our nation - are a threat to national security," said Lena Masri, the group's national litigation director. "This is an order that is based on bigotry, not reality."
During the past budget year, the US accepted 84,995 refugees, including 12,587 people from Syria. President Barack Obama had set the refugee limit for this budget year at 110,000.
According to Mr Trump's executive order, he plans to cut that to 50,000.
Jan Egeland, of the Norwegian Refugee Council, said the decision "will not make America safer, it will make America smaller and meaner".
He said the decision dealt a "mortal blow" to the idea of international responsibility for those fleeing persecution.
The US is leading a "race to the bottom" in which politicians in wealth countries provide "zero moral leadership", he said.
Malala Yousafzai, shot in the head by the Pakistani Taliban in 2012 to stop her campaigning for girls' education and co-winner of the 2014 Nobel peace prize, said she is heart-broken by the ban.
Ms Yousafzai implored Mr Trump "not to turn his back on the world's most defenceless children and families".
Refugees and immigrants, she said, have "helped build your country".