Enda Kenny and David Cameron have agreed to start immediate diplomatic talks on the issues of common travel and an Irish border.
The two leaders have spoken after the result in the Brexit referendum, which has prompted David Cameron to resign.
The premier will step down in time for a new leader to be chosen at the Conservative Party's conference in October.
It will be up to that leader to begin the two-year Article 50 process - known informally as the 'divorce talks' - which will determine the terms and conditions of Britain's exit.
In their 12-minute phone conversation this evening, Enda Kenny told Cameron he understood his wish to leave the divorce talks to a pro-Brexit successor.
"It was agreed that it would be priority that there would be no interruption to the close bilateral work at political and official level on Northern Ireland," a statement said.
"Moreover, it was agreed that there would be immediate bilateral contact between senior officials on the issues of mutual interest arising from the referendum, including the common travel area and the border."