Formal negotiations between Barnier and British Brexit minister David Davis had been due to start next week but that timetable has been thrown into doubt by May's catastrophic loss of a majority in last Thursday's election.
Mrs May's authority has been severely diminished after a disastrous general election which saw her lose her Commons majority and a deal with the DUP looks vital for the continuation of Tory rule.
Labour leader Jeremy Corbyn countered with a bit of previously unseen swagger, wearing a huge red rose - his party's symbol - in his lapel as he sparred with May and taunted her about the uncertainty surrounding the upcoming vote on her legislative program, known as the Queen's Speech.
Her most senior minister Damian Green has confirmed the Queen's Speech setting out the Government's programme could be delayed if a deal is not reached in time for it to go ahead on Monday as planned.
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
"I think there will be pressure for a softer Brexit, Cameron said during a business conference in Poland, adding that Parliament "deserves a say" on how to manage the process".
The talks with the DUP follow her apology to Conservative rank-and-file lawmakers in a meeting for the party's poor election result.
British Prime Minister Theresa May's Conservative party resumed talks on a deal to prop up her minority government on Wednesday as she faced a battle over her Brexit strategy just days before European Union divorce talks are due to begin.
European politicians also appeared to detect a shift in the mood around Brexit, with France's Macron saying the door was open until the negotiations had concluded for Britain to remain a member of the EU. The Evening Standard, edited by ex-Treasury chief George Osborne, is reporting that Cabinet ministers have initiated talks with Labour lawmakers.
DC police say 2 arrests made in Turkish embassy melee case
The NATO allies have publicly clashed over a US decision to arm Syrian Kurdish rebels fighting the Islamic State group in Syria. Lawmakers responded with outrage at the time, saying that political violence wouldn't be tolerated on US soil. -Turkish ties.
Mr Adams, addressing claims of Sinn Fein disengagement, said: "We want into the institutions, because that is what the people desire, that is what the people voted for".
Major said his list of concerns included how a post-Brexit Britain would resolve the issue of the Northern Ireland border with Ireland, the UK's only land border with the European Union.
Saying he supported May and could understand why she sought the DUP deal, Major argued it was a mistake. "That does worry me a great deal about the peace process", he told BBC Radio 4.
The stakes for May are high.
In the briefing they said the prospect of an agreement between the Conservative Party and the DUP was causing "anxiety and fear" over fears that any deal agreed on would affect issues relating to Northern Ireland.
Mr Corbyn added: "I must let the House know - and the rest of the nation know - that if that is not possible, the Labour Party stands ready to offer strong and stable leadership in the national interest". Michel Barnier warned that no progress had been made in the three months since May triggered Article 50 to start the process of leaving the union.
"But let us be clear and organised and once the negotiations have started we should be well aware that it'll be more hard to move backwards".
But in an article for the Financial Times, the EU's chief negotiator Michel Barnier has warned the United Kingdom that there is "no time to waste" to get the process - which has 18 months to run - under way.
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