"The most right-wing and reactionary party in northern Ireland will be backed by the most right-wing and reactionary major party in Britain, directly the product of British imperialism's history of intervention and domination in Ireland", he commented, pointing out that the UDA and UVF paramilitaries had backed the DUP in this month's General Election.
Mr Coveney met all the five main political parties and Northern Ireland Secretary James Brokenshire in what was his first involvement in the process since replacing Charlie Flanagan at the head of the Department of Foreign Affairs in Dublin last week.
Mr Coveney pledged to "spare no effort" to help get the Stormont power-sharing Executive back up and running.
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.
Mr Varadkar said he was "very reassured" by her commitment to make public the terms of any deal.
The DUP had made it clear, he added, that they did not want "an unstable government undermining our union" and wanted to see us "go ahead with the Brexit negotiations with a sensible government in place".
Grainne Teggart, Campaign Manager for Amnesty International in Northern Ireland, said: "Today's results confirm what we have long known: that an overwhelming majority favour reform of our inhumane abortion laws".
Senior DUP representative and former Stormont minister Simon Hamilton also struck a positive tone during a day that saw the first round table plenary session of a talks process that started last week.
The Sinn Féin National Chairperson also accused the Irish Government under Enda Kenny of a "dereliction of public leadership".
"I'm a Northern Ireland native journalist and can't find full time paid work, but someone at Sky News Australia thinks Sinn Fein is a person", wrote Twitter user Aoife-Grace Moore. "So I'm afraid to say there is no goodwill towards her".
May told journalists the United Kingdom government remained "absolutely steadfast" in its commitment to the Belfast Agreement and that discussions were continuing with the DUP over a confidence and supply agreement, which would see the unionist party's 10 MPs back May's government on key votes.
She said: "We continue our discussions with the DUP".