Democratic Unionist leader Ian Paisley and the Irish prime minister Bertie Ahern are to visit the historic site of the 1690 Battle of the Boyne.
Ian Paisley and Bertie Ahern shook hands in public for the first time
Mr Paisley said it would show "how far we have come when we can celebrate and learn from the past".
He was speaking after talks with the taoiseach in Dublin when the pair shook hands publicly for the first time.
Mr Paisley said he hoped "old suspicions and discord can be buried forever" through mutual co-operation.
The Battle of the Boyne was fought between William of Orange and Catholic King James II in 1690. The Protestant Orange Order celebrate William's victory every year on 12 July.
Mr Paisley said: "We both look forward to visiting the battle site at the Boyne, but not to re-fight it. I don't want Mr Ahern to have home advantage."
He added: "As the leader of the unionist people, with Northern Ireland's place in the union secured, I believe it is important to engage with our closest neighbour from a position of mutual respect and with assured confidence.
The annual 12 July celebrations mark the Battle of the Boyne
"Today, we can confidently state that we are making progress to ensure that our two countries can develop and grow side by side in a spirit of generous co-operation.
"Old barriers and threats have been, and are being, removed daily."
Mr Ahern told the same news conference: "We stand ready to work with the new executive.
"We promise sincere friendship and assured co-operation and I believe we can and we will work together in the interests of everybody on this island.
"We look forward to our cooperation in the north south, and the east-west institutions and in all those areas where we can work together for mutual benefit."
Earlier, Mr Paisley, accompanied by son Ian Paisley Jr, shook hands with the Irish premier, saying: "Good morning. I better shake hands with this man and give you a firm grip."
Meanwhile, Irish foreign minister Dermot Ahern said the Northern Ireland parties had "grasped the opportunity of a lifetime" by agreeing to share power.
However, he said much work remained to be done.
Mr Paisley and Sinn Fein president Gerry Adams announced at their first joint news conference last week that they agreed 8 May as the date to start power-sharing at Stormont.
Dermot Ahern said last week's meeting "saw a shift in the political paradigm of Northern Ireland".
"The parties grasped the opportunity of a lifetime and committed themselves to support and participate fully in a partnership government and in all of the institutions of the Good Friday Agreement.
"Restoration of the power-sharing institutions on 8 May, as now agreed by the parties, will mark major progress, but it will not be the end of the road."