Peter Robinson and Martin McGuinness say they have spoken to Fine Gael leader Enda Kenny to congratulate him on his party's general election success, which put him on course to become Taoiseach.
The First Minster said: "I look forward to working with Mr Kenny over the coming period. I will be watching closely developments in the Republic as the new government sets about its difficult task of rebuilding a stable economy."
Deputy First Minister Mr McGuinness added: "The election result has significantly changed the political landscape and over the coming weeks and months we will look to build and strengthen our relationship with the new government in the South. It is clear that there are many areas where we can work together constructively for the betterment of all the people of Ireland."
Earlier, DUP leader Mr Robinson said floating unionist voters concerned at Sinn Fein's southern surge may flock to his party to help block republicans north of the border.
Meanwhile, Sinn Fein Deputy First Minister Mr McGuinness said attempts by SDLP leader Margaret Ritchie to undermine his party in the Republic had backfired.
The salvos were launched as Northern Ireland politicians, preparing for local government and Assembly elections on May 5, calculated the likely impact of Sinn Fein's success in trebling its Dail representation.
Mr Robinson, who was unveiling his team of Assembly candidates at Stormont, said: "I listen to what the pundits say, and clearly there will be something of a bounce for them (Sinn Fein).
"But the pundits are equally saying that there will be a bounce for us because people will want to ensure that they stop Gerry Adams in his tracks with his all-Ireland plan."
Mr Robinson characterised Sinn Fein's surge as being the result of a protest vote by an electorate that was angry over the mishandling of the Republic's economy.
"They will end up being something of a contradiction. It will be very difficult for them to take the irresponsible role that oppositions often take in the south, and to take the responsible role that governments have to take in Northern Ireland," said the DUP leader.