Senator Aodhan O Riordain was speaking as speculation is increasing that the US president will visit Ireland in early June.
Mr Trump will make a three-day state visit to the UK from June 3-5.
He is expected to travel to France on June 6 to attend commemorations to mark the 75th anniversary of D-Day at the Normandy American Cemetery.
It is anticipated that Mr Trump will base himself in Ireland after leaving the UK, in what is thought will be primarily a private visit centred on his golf course at Doonbeg in Co Clare.
The visit has not yet been confirmed by the Irish Government or the White House.
It is understood that US officials based in Ireland are to be briefed on the matter in the coming days.
Irish Premier Leo Varadkar said he could not confirm a visit to Ireland by Mr Trump, as the White House would make such an announcement.
He told RTE: “If President Trump comes to Ireland he will be treated with respect and given the welcome his office deserves.
“The President of America is always welcome in Ireland, just as the Taoiseach and Irish President are welcome in the United States. We’ve a really strong relationship, it’s economic, it’s cultural, it’s historic. It’s about our family connections as well.
“I think we have to rise above whoever holds the office, whether it’s the office of President there or here or Taoiseach and remember the really important relationship that exists between Ireland and America. That has to be the priority.”
Mr Trump has previously spoken of his love of Ireland.
In March, when Mr Varadkar visited the US president in Washington DC, Mr Trump spoke of his plans to visit, and described the Irish as “truly wonderful people”.
He had been expected to visit Ireland last November but that was cancelled with the US side citing scheduling reasons.
However Mr O Riordain said on Wednesday that the Irish people do not want Mr Trump to visit.
“When he announced a visit previously he quickly cancelled when the level of public resistance to it became clear,” he said.
“Now he intends to visit for a few days in June. We know the only reason he wants to come here is to exploit the visit for electoral purposes with the large Irish-American electorate.
“There are deep and permanent bonds of friendship between the peoples of Ireland and the United States and usually a president is warmly welcomed. But Trump is no ordinary president.
“It must now be the absolute focus of all peace-loving democrats in Ireland to oppose this visit.”