Mr Coveney did not want to participate in Taoiseach Leo Varadkar's talks with the US President, as they involved the impact of Brexit on Ireland.
The two men are holding a meeting at the airport, with Brexit, immigration, trade, USA support for Northern Ireland, and the E3 visa programme expected to be discussed.
"I think I make up for it right now", he said.
And now President Trump, who has called global warming a "Chinese hoax" and pulled the United States out of the Paris climate agreement, appears similarly unmoved by an appeal from British royalty.
In the video, obtained by The Sun, Dalla Mura then approaches people in the crowd and says: "I think Donald Trump's balloon is not very well, I think it's going down rapidly for a reason".
Reading from the prayer, Trump said: "Almighty God, our sons, pride of our nation, this day, have set upon a mighty endeavor, a struggle to preserve our republic, our religion and our civilization and to set free a suffering humanity".
He said ahead of the meeting: "It's no secret that we don't agree with President Trump's views on Brexit".
The meeting with business leaders at St. James' Palace will bring together 10 leading companies - five from the UK and five from the United States. Many in Ireland express worry that if the United Kingdom does leave, a "hard border" will return between Ireland and Northern Ireland, which is part of the U.K, potentially reigniting sectarian tension that lasted for decades and sometimes exploded into violence. He added the timing of their meeting was important as Trump would have heard "a certain story" from pro-Brexit lawmakers during the first stop-off of his European trip in Britain.
He accepted an invitation from Mr Varadkar to visit Ireland while in Europe to attend events in Britain and France commemorating the 75th anniversary of the D-Day landings.
Trump is on his first visit to the country as president.
Trump touched down at Shannon Airport in the West of Ireland on Wednesday.
She continued: "Dear Mr Trump". Otherwise there's slight acquiescence - that's the new normal, that's acceptable.
"I think you do, I think you do", Trump responded.
Labour TD Jan O'Sullivan said that public representatives have a duty to protest against Mr Trump's visit.
"When the state visit was announced we were suddenly inundated with messages saying "you've got to fly the baby again", Mr Murray said.
Mr. Trump avoided the USA military draft in place during the war by getting a medical deferment for bone spurs.
"Respectfully... reminds the President of the existing USA commitment as a guarantor of the 1998 Good Friday Agreement and asks that its fulfilment and the delivery of lasting peace in Ireland must be a precondition to any future US/UK trade deal", they said.
Trump was scheduled to visit Ireland previous year but the trip was abruptly cancelled.
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