Leo Varadkar had expressed concern about a possible deal between the Conservative party and the DUP.
"We spoke about the very important need for both governments to be impartial actors when it comes to Northern Ireland and that we are co-guarantors of the Good Friday Agreement and that any agreement that may exist between the Conservatives and the DUP should not in any way impact on the Good Friday Agreement", he said.
Referring to financial controversies which helped tumble the Executive earlier this year, including the Cash for Ash scandal linked to Ms Foster, Mr Kearney said they continue to overshadow the region.
As he travelled to Belfast to participate in negotiations for the first time, Simon Coveney pledged to "spare no effort" in the process to salvage the crisis-hit institutions at Stormont.
"Obviously also we are going to have a discussion around Brexit".
She is seeking to negotiate a so-called "confidence and supply" arrangement whereby the DUP will throw their weight behind the government in key Commons votes, such as on the Queen's Speech and Budgets.
She said: "We want to see an administration set up again that will last and one that will last for all of the people of Northern Ireland".
A DUP source confirmed negotiations were "ongoing" and said they were looking to deliver "a more compassionate style of government for the whole of the UK".
The participants have until June 29 to reach a deal that would see devolution returned or they face the prospect of direct rule being reimposed from Westminster.
If a new executive is formed it should ideally include the SDLP, Ulster Unionists and Alliance Party, said Mr Coveney.
The two dominant parties in Northern Ireland, Sinn Fein and the DUP, both have terrorist origins and once killed each other.
The Irish CP leader said that the DUP are in a contradictory position, aiming to maintain the division of Ireland while also seeking to locate the economic border between the United Kingdom and the European Union "down the middle of the Irish Sea" alongside the security border.
I may have worked in many cultures and countries in the interest of our country, but in Parliament I'm still new.
DUP senior negotiator Simon Hamilton hoped that the DUP-Tory talks would conclude soon. "We are hopeful of getting resolution to them as quickly as we possibly can".
She said: "We remain fully committed to making the institutions work".