The embassy also says there is no change to the Visa Waiver Program
The US embassy in Dublin has confirmed Donald Trump's travel ban does not restrict the travel of Irish dual nationals.
The embassy says they will be unaffected so long as they hold the passport of an unrestricted country and possess a valid US visa.
There are also no changes to the Visa Waiver Program (VWP) for Irish people.
However, those who hold dual nationality of Iraq, Iran, Syria, and Sudan are not eligible for the Visa Waiver Program and must have a visa for travel.
The embassy says this was in place before the executive order restricting travel.
"Such individuals may apply for a visa as needed at a US Embassy or Consulate. Dual nationals of Yemen, Libya, and Somalia and a VWP country may continue to travel under the VWP unless they have travelled to any of the seven countries on or after March 2011, in which case they must first apply for a US visa", the embassy says.
"The Executive Order does not restrict the travel of dual nationals from any country, so long as they hold the passport of an unrestricted country and possess a valid US visa, if required", it adds.
Meanwhile Taoiseach Enda Kenny says he will not write to Donald Trump to oppose his executive order on immigration.
Mr Kenny says this is because he will raise his concern in person.
But he says he is willing to sign up to an all-party Dáil motion, outlining Ireland’s opposition to the clampdown.
Opposition leaders in the Dáil want the Taoiseach to write directly to Mr Trump to complain about the new policy being imposed on Irish soil.
Mr Kenny said: "I have not written to the United States president because I intend to visit him in the Oval Office in the White House and say my piece publicly, both before and then.
“I think President Trump is well used to disagreements and obviously is going to have many more in the time ahead", he added.
He also told the Dáil the new US immigration policy is "morally unacceptable".
While following talks with British Prime Minister Theresa May yesterday, Mr Kenny said: "In respect of the policies introduced by the American government – I disagree with it.
“I obviously will say that to the president and vice-president when I meet with them.”
It came after the Department of Transport said one person had been stopped from travelling to the US under the new rules.
It has since been confirmed that the person turned away from pre-clearance in Dublin was already a resident here and allowed to remain.
Yesterday, the Taoiseach called for a "complete review" of the running of the United States' immigration preclearance facilities in Ireland.
The Cabinet has been considering the review, and the matter is set to be debated in the Dáil.
The Labour leader putforward a Private Notice Question to the Taoiseach, with such questions "reserved for matters of urgent public importance".
Deputy Howlin argued that the many are concerned the US is intending to operate an order that "blatantly discriminates on grounds of religion and that also abandons US international legal obligations to asylum seekers".
He will ask the Taoiseach to address "if in particular the perception of collusion in [preclearance] implementation inhibits the Taoiseach’s ability to robustly articulate Irish opposition to these policies, as he has already committed to do".
Meanwhile, the Anti-Austerity Alliance / People Before Profit are tabling a Dáil motion for the Taoiseach to cancel the annual St Patrick’s Day trip to White House.
Mr Kenny has indicated he will make the trip in March, but AAA/PBP says the only way to 'register our opposition' to the immigration policies is to not attend the White House event.
The motion also calls for a commitment to ensure that Irish officials do not facilitate the immigration policy at airports here.
Paul Murphy argues: “We will be demanding today that this motion is debated in the Dáil. Racist, anti-Muslim policies are being implemented in airports in Ireland, [and] there must be a discussion in the Dáil on it immediately."
His colleague Ruth Coppinger adds: "There have been inspiring protests against these policies across the US, and a partial strike by New York taxi drivers.
"We would support any airport workers in Ireland who refused to assist in the implementation of these policies."