Northern Ireland First Minister Peter Robinson said he hoped people would show the same respect to the Queen during a visit to the Republic as he did to President Mary McAleese.
The DUP leader met Ms McAleese in Dublin prior to the North-South Ministerial Council meeting in Farmleigh and briefly touched on the potential for a royal visit.
The British and Irish governments are planning the Queen's first state visit to Ireland before the end of next year.
Mr Robinson said: “We had a brief discussion, obviously, about the potential for a royal visit, which I would welcome, and I hope that the respect that I showed to the head of state here will be shown by others to the head of state from the United Kingdom.”
After a meeting with Prime Minister David Cameron in London last month, Taoiseach Brian Cowen said he wanted to see the official engagement before Ms McAleese leaves office.
Mr Cowen said there was now no obstacle in the way of Queen Elizabeth coming to Ireland.
Sinn Fein's leader in the Dail Caoimhghin O'Caolain later said Mr Cowen's welcoming of a visit was totally unacceptable.
When asked if he would discourage Sinn Fein members from protesting at a visit, Deputy First Minister Martin McGuinness said the focus should be on the Farmleigh meeting.
“I think Sinn Fein spokespersons have spoken about that in the course of the last couple of weeks,” he admitted.
“We're here today to talk about the work of the North-South Ministerial Council and that's where I think the focus should be.”