Sinn Féin's Martin McGuinness told the outgoing Democratic Unionist Party (DUP) leader that all political careers end and added: "My day too will come."
Mr Robinson quickly interrupted him to say: "That's Tiocfaidh ár Lá isn't it?"
The DUP leader was referring to the Irish republican slogan which translates as "Our day will come".
Mr McGuinness replied that he was delighted Mr Robinson's knowledge of the Irish language was improving.
He wished the first minister well in his forthcoming retirement and praised his track record of leading the Northern Ireland Assembly since 2008, despite their different ideologies and allegiances.
"It hasn't all been trouble-free, we have faced huge challenges," Mr McGuinness said.
"It was never going to be plain sailing but I think the fact that we kept the institutions intact for eight years - they didn't collapse on one occasion - was a tremendous indication of our commitment to ensuring that the institutions, that are so embedded in the peace process, continue to work for people so that we can build a better future for all of them," he added.
Irish Prime Minister Enda Kenny said his government had presented Mr Robinson with nine volumes of Irish biography and football tickets to a Tottenham Hotspur v Arsenal match as a farewell gift.
Mr Kenny said: "I want to pay public tribute to Peter Robinson as a political engine and driver over very many years, who has left his imprint on Northern Ireland politics and on the politics of this country and on the political landscape.
"I wish Peter the very best in his retirement."
The Irish Foreign Minister Charlie Flanagan said he had personal experience of the DUP leader's "great contribution" to Northern Ireland politics at the recent Stormont talks.
"There were occasions that gridlock and deadlock was avoided because of the intervention and leadership of Peter Robinson," Mr Flanagan said.
During Friday's meeting, the two administrations reviewed the political progress made at the Stormont talks that resulted in a new agreement between both governments, the DUP and Sinn Féin.
Mr Robinson said: "The Fresh Start [Agreement] has got off to a good start."
Mr Flanagan also repeated his government's commitment to the A5 road project between Londonderry and Dublin.
There have been tributes, retirement gifts and laughter at Peter Robinson's final appearance at the North South Ministerial Council.