As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.
The DUP is believed to be more favourable to a "soft Brexit" that would keep Northern Ireland's border with the Republic of Ireland free-flowing.
Gerry Adams has warned Theresa May that her possible deal with the DUP is playing "fast and loose" with her government's commitment in the Good Friday agreement to be impartial.
She has already met with the DUP to seek a deal to support a minority Conservative government.
Guy Verhofstadt, the European Parliament's chief Brexit negotiator, warned Tuesday that "the current uncertainty can not continue" and on Wednesday issued five "pressing questions" on Twitter.
The Conservatives need the DUP's 10 votes to achieve a working majority in parliament but some politicians and commentators have expressed fears that it could undermine the peace settlement that brought an end to three decades of violence in Northern Ireland.
But a newly appointed junior Brexit minister, Steve Baker, told Reuters: "I don't foresee any change".
Macron's pro-EU party set for sweeping victory in French parliamentary election
Prime Minister Edouard Phillipe, who was appointed by Mr Macron last month, announced " France is back" as the results rolled in. Macron was seeking a majority of the 577 seats for his centrist party, Republic on the Move, in the first round of voting.
British Prime Minister Theresa May is edging closer to clinching a deal to stay in power with the support of Northern Irish kingmakers but faces a battle over Brexit just days before divorce talks are due to begin.
Seven MPs were elected in Sinn Féin colours last week, although the party has always refused to take up seats in Westminster.
Northern Ireland has been without a powersharing executive since March and without a first and deputy first minister since January, after Sinn Fein collapsed the administration amid faltering trust and relations with the DUP.
Barnier dismissed the suggestion of postponing the negotiations and said such a delay would only prompt further instability. "We are impatiently waiting for the negotiating position of the United Kingdom gov (ernment)".
France's Macron said the EU's door was still open for Britain as long as the negotiations were not finished, but that it would be hard to reverse course.
The draft law would empower Europe to decide if post-Brexit London has the right to host financial market "clearing houses" that deal in euros, the EU's single currency.
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