Sinn Fein, which won seven seats in the British parliament at last week's election but will maintain its policy of not taking them, said its leader in Northern Ireland, Michelle, O'Neill would repeat those concerns in London on Thursday.
For Labour, shadow business secretary Rebecca Long-Bailey said the prospect of a Conservative-DUP deal was "worrying", telling BBC Radio 4's Today programme: "It would create a lot of instability in terms of the peace process in Northern Ireland".
May has given no indication she will change course on the key elements of Brexit; but whatever her plan she will be heavily reliant upon the 10 lawmakers from the eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing.
Talks with the DUP broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
A spokeswoman for the DUP said they hope talks will be "coming to a conclusion soon", but the negotiations have raised eyebrows with former Prime Minister John Major questioning the impact on the Northern Irish peace process.
The anticipated deal with the DUP has forced Mrs May to reject claims that the Government will fatally undermine its supposed impartiality in Northern Ireland, in particular in the ongoing process to restore Stormont powersharing.
The proposed "supply and confidence" deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week, as well as change Britain's entire approach to its EU withdrawal.
"It's going to be hard".
Police official IDs UPS warehouse shooter
Nor did Brent Andrew, spokesman for Zuckerberg San Francisco General Hospital, which had received the victims. Dozens of UPS employees were escorted from the facility under police guard, according to witness accounts.
Parliament now "deserves a say", he said, adding that there was "perhaps an opportunity to consult more widely with the other parties on how best we can achieve it".
He also suggested that the Scottish Tories led by Ruth Davidson could also add to the pressure on Mrs May to change course.
The Times newspaper said finance minister Philip Hammond would push May not to leave the customs union - an arrangement which guarantees tariff-free trade within the bloc but prohibits members from striking third-party trade deals.
That would help safeguard jobs and trade with European Union members, but would severely restrict the UK's ability to strike its own trade deals around the world.
Mrs May was in France for talks with the French President.
He said: "Of course the door remains open, always open until the Brexit negotiations come to an end".
She said: "I think there is a unity of objective among people in the United Kingdom".
Demanding a swift start to Brexit negotiations under Article 50 of the European Union treaties, the former Belgian prime minister compared Britain's position to the heroine of Lewis Carroll's Alice In Wonderland, who found herself in a room with many doors and no idea what lay behind them.
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