Sinn Fein's Stormont leader Michelle O'Neill said: "I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements".
With her tally of Conservative MPs slashed to 317 in last week's poll, Mrs May needs the backing of the DUP's 10 members to reach the 320 required for a working majority in the Commons.
And as protracted negotiations between the ruling Conservative Party and a small Northern Irish party remain unresolved, a meeting with another party from the province is set to add further confusion to proceedings.
The DUP is not demanding the United Kingdom stays in the customs union as the price for supporting Prime Minister May, the Financial Times reported, without citing anyone.
European Central Bank leaves base interest rates unchanged
While few expect that to happen, the words underline that the bank is not yet willing to call time on the stimulus program. The euro-area economy grew faster at the start of the year than previously estimated as domestic demand bolstered output.
France's Macron said the door was still open for Britain to remain in the European Union, though he added that it would be hard to walk back once negotiations start.
"If we had a strong signal that she were backsliding, I think she would be in major difficulty", the newspaper quoted one unidentified former minister as saying.
Earlier, Andrea Leadsom, leader of the lower house of parliament, said the government had agreed with Queen Elizabeth, who reads out the new government programme, that the "state opening of parliament will take place on 21 June 2017".
A senior Conservative Party source said the talks were ongoing.
The Conservative source said: "We're confident of getting an agreement, we're confident that the Queen's speech will be passed". Even before May had called and lost last week's election, Juncker had told her that she had a very tiny and uncertain majority of seven deputies in the Parliament to reckon with the the Herculian task she had to accomplish - to leave the EU and agree the future relations with the Union.
A quick look at the French Open
Pliskova, the Czech, beat Carina Witthoft of Germany 7-5 6-1, while Svitolina of Ukraine overcame Poland's Magda Linette 6-4 7-5. The Serb needed 75 minutes to clinch the opening set but then outclassed the 19th seed to set up a showdown with Dominic Thiem .
Northern Ireland has enjoyed peace and prosperity for a long time now let us hope this continues.
However, putting the pro-British unionist DUP in a position of influence in London could also undermine the British government's ability, enshrined in a 1998 peace agreement, to function as an impartial broker between Northern Ireland's unionists and its Catholic Irish nationalists.
"They will want to get whatever they can out of the Government for Northern Ireland and will go in with the approach of "make us an offer", then "make us another offer" until they are happy".
"She doesn't have a mandate for scrapping the winter fuel allowance, or taking hot meals away from children, and there could be support for other things too, such as scrapping the bedroom tax", the source said.
The newspaper quoted another former minister as saying: "If she weakened on Brexit, the world would fall in. all hell would break loose".
US Open: Brooks Koepka wins 117th US Open
South Korea's Kim Si-Woo is one back on nine under, just ahead of Patrick Reed, Charley Hoffman and Russell Henley on eight under. Open clubhouse leader, though at five under par Steve Stricker eventually finished 11 strokes behind victor Brooks Koepka.
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