Mr Coveney, who lost out to Leo Varadkar in the race to succeed Enda Kenny as Fine Gael leader and Taoiseach, has replaced Charlie Flanagan at the head of the Department of Foreign Affairs in Dublin.
Varadkar said he would emphasize to May the British and Irish governments must remain impartial in Northern Ireland, as stipulated by the Good Friday Agreement.
It is a week since DUP leader Arlene Foster visited Downing Street for talks with Theresa May, with reports that a final agreement is being held up by discussions over extra funding for Northern Ireland. "We are talking about a confidence and supply agreement with them", she said.
She has also cancelled next year's Queen's Speech due to Brexit, with parliament to sit for two years instead of the usual one.
"We made the case to her that we would oppose any deal that undermined the Good Friday Agreement", he said.
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He scored 42 goals in all competitions and played a key role in helping his club win the Champions League and the La Liga . However his opponents criticised reforms in the club statutes which have toughened criteria for aspiring candidates.
"If there is the expected positive outcome, it will be at least the start of next week before anything is signed off", a DUP source said.
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.
The comments were seen as a coded reference to the party's opposition to scrapping the "triple lock" on pensions and means testing the winter fuel allowance - both of which were in the Conservative manifesto.
Irish Minister for Foreign Affairs, with special responsibility for Brexit, Simon Coveney said he welcomed the negotiations, which are not only important for the European Union and Britain but "are one of the most important set of negotiations in the recent history of our country".
In March's assembly elections in Northern Ireland, the unionists emerged for the first time ever without a majority, with the pro-republican Sinn Fein making massive gains.
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Fultz led the Pac-12 in scoring and finished No. 6 among all Division I players, and was the top freshman scorer in the country. Be proactive - Use the "Flag as Inappropriate" link at the upper right corner of each comment to let us know of abusive posts.
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.
"Over the coming months, I will work to ensure these negotiations protect and advance Ireland's interests and deliver the best outcome for our people, for our businesses and for our island".
Asked if his party favoured a hard or soft Brexit, Mr Hamilton said the preference was for a "sensible Brexit".
O'Neill told reporters outside the Dail they are also committed to getting a government up and running in the North.
"We are working away at them and will continue to work away at them".
UK Fraud Office charges Barclays over Qatar fund-raising
All have been charged with conspiracy to commit fraud by false representation in relation to the June 2008 capital raising. Barclays said it was considering its position over the charges and awaited further information.