Theresa May has still not secured a deal with the Democratic Unionist Party to allow her Government programme to survive a Commons vote, a day before the Prime Minister sets out her legislative measures in the Queen's Speech.
The remarks came after warnings by the nationalist Sinn Fein and SDLP and the cross-community Alliance Party that a deal with the DUP would undermine the Government's attempts to restore the powersharing executive at Stormont.
Speaking at a joint news conference with May, the Republic of Ireland's new Prime Minister Leo Varadkar said that the border should be "invisible".
Mr Coveney said a deal was "do-able" but there were differences between the parties that needed to be bridged.
But May's failure to win a majority in last week's election has weakened her position badly and reopened the debate around the Brexit strategy just days before the country opens its divorce talks with Brussels on Monday.
But Stormont parties have a June 29 deadline to end the impasse and reach consensus on re-establishing a devolved administration in the region.
The comments were an apparent reference to the party's opposition to scrapping the "triple lock" on pensions and means-testing the winter fuel payment, both of which appeared in the Conservative manifesto.
Mr Kearney said his party's equality and rights agenda "is not negotiable".
"The talks are going on but one thing I am absolutely certain of is that the DUP do not want to see another election and Jeremy Corbyn in Downing Street", he said.
The two dominant parties in Northern Ireland, Sinn Fein and the DUP, both have terrorist origins and once killed each other.
THE IRISH Government has warned there could be disaster ahead for Ireland if Britain fails to secure a deal to withdraw from the European Union by March 2019.
Senior DUP representative and former Stormont executive minister Simon Hamilton insisted any deal with the Conservative Party would benefit the whole of the United Kingdom, not just Northern Ireland.
So I would suggest we become more demanding of those who are elected to take responsibility that they do so constructively.
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. "We are hopeful of getting resolution to them as quickly as we possibly can".