The Cabinet is split over whether official meetings should be arranged with US presidential candidate Donald Trump when he visits Ireland later this month.
Mr Trump's announcement yesterday of his plans to visit Doonbeg in Co Clare took senior government figures by surprise.
The visit will take place around the same time that British voters take part in the EU referendum and US Vice President Joe Biden's official trip to Ireland.
Mr Trump's planned visit immediately became shrouded in controversy as a result of his previous comments about women, Muslims and Mexicans.
During a Dail debate last week, Taoiseach Mr Kenny labelled Mr Trump "racist" and "dangerous".
Mr Kenny, Tanaiste Frances Fitzgerald, Finance Minister Michael Noonan and Foreign Affairs Minister Charlie Flanagan refused yesterday to commit to meeting the controversial US businessman.
However, several ministers broke rank and refused to stick to the Government's official line that was issued from the Taoiseach's office.
"Mr Trump, like every tourist, will be more than welcome to Ireland and we hope he has a pleasant stay," the response said.
Despite describing Mr Trump's attitude towards women as "misogynistic", Social Protection Minister Leo Varadkar said he would meet the presumptive Republican candidate in the race for the Oval Office.
"I meet people I disagree with all the time. I'd also say what I said to his face," Mr Varadkar told the Herald.
His Fine Gael colleague, Agriculture Minister Michael Creed, agreed.
"The minister understands that Mr Trump is visiting in a private capacity. Minister Creed is willing to meet with visitors if requested to discuss potential trade opportunities for the Irish agri-food sector," said Mr Creed's spokesman.
Minister for Disabilities Finian McGrath criticised the idea of government ministers shunning Mr Trump.
He emphasised that while he does not agree with all of Mr Trump's political views, he likened the idea of shunning the billionaire businessman to "modern-day political correctness".
"I don't believe in the business of not talking to people," he said.
A spokesman for Communications Minister Denis Naughten said he believes a meeting with Mr Trump "would result in an interesting political debate".
People Before Profit TD Richard Boyd Barrett launched a stinging attack on Mr Trump, who he described as a "dangerous and vile racist", a "warmonger" and "sexist", and said he and his colleagues will be holding a protest during the visit.
The Labour Party has also objected to formally welcoming Mr Trump when he visits the hotel and golf resort he owns in Doonbeg.