DUP leader Arlene Foster has said the Taoiseach needs to accept that Brexit is going ahead.
She also accused Leo Varadkar of being "unhelpful" by making comments about the border after the UK leaves the European Union.
Although relations between the Democratic Unionists and the Irish government remain strained, Mrs Foster said she was looking forward to meeting Mr Varadkar on Friday when he makes his first visit to the North since taking over as Taoiseach.
While in the region Mr Varadkar will attend a gay pride event in Belfast on Saturday morning to promote the rights of the LGBT community.
Although Mrs Foster's party is strongly opposed to same-sex marriage she said that Mr Varadkar is "perfectly entitled" to attend the event.
Speaking following an event at the former Maze Prison outside Lisburn on Wednesday, Mrs Foster rubbished Mr Varadkar's hope that the UK will U-turn on Brexit and remain within the European Union.
The Taoiseach said this week he remained "hopeful" that Brexit would not happen.
However, Mrs Foster told reporters this was "disrespecting" the wishes of the British people.
"He may be hopeful but that is disrespecting the will of the British people. Brexit is going to happen. We are leaving the European Union.
"I just hope the Republic of Ireland will continue to work constructively with us in Northern Ireland and the rest of the UK because it is very much in their interest to have a Brexit that works for them as well as a Brexit that works for the UK," the former Stormont first minister said.
Mr Varadkar angered unionists when he said Ireland would not help the UK design an economic border for Brexiteers.
Mrs Foster said the comments were "not helpful" and added that the Irish Government "should reflect on whether they are being helpful to the process here in Northern Ireland or not".
She continued: "They have made various interventions recently in relation to Northern Ireland politics. It would be better if we focused on finding solutions to what is in front of us. We want to find ways forward.
"We know there are huge opportunities in relation to Brexit and we also accept there are short-term challenges. To overcome all of that we have to work together. The sort of megaphone diplomacy that has been engaged in is not helpful. We have to work together to get a European exit that works for everybody."
She added that she will be raising a "number of issues" with Mr Varadkar on Friday and that she was "looking forward to the meeting".
When asked about his planned attendance at the gay pride breakfast on Saturday, she responded: "He is perfectly entitled to come and attend whatever he wants. I go to the Republic of Ireland and attend events down there so he is perfectly entitled to do that here."