Reports suggested that the Queen's speech and Brexit negotiations could be delayed as a result. European Union leaders gave chief negotiator Michel Barnier no authority to so much as talk about trade until he clinches outline deals on Brussels' priority issues, including on what London owes them.
May's government has said its Brexit plans remain the same, and will be pressing for close economic ties but a clear break with the bloc to be able to control immigration and restore sovereignty over British laws.
The talks later continued at Westminster without Theresa May after she left for Paris for a pre-arranged meeting with newly-elected French president Emmanuel Macron.
Theresa May has signalled she is "confident" of getting the Queen's Speech through the Commons whether or not a deal is reached with the Democratic Unionists (DUP) by the State Opening of Parliament next week.
Referring to claims from Sinn Féin that a deal with the Conservatives could represent a breach of the Belfast Agreement, she said she would advise people to read the agreement.
"The door of course is still open as long as Brexit negotiations have not been concluded", he said.
The EU will keep the door open for Britain to return, but only on worse terms than it now has, European Parliament Brexit negotiator Guy Verhofstadt said Wednesday.
If the parties can not agree a deal, then devolution will be suspended and the Northern Irish assembly's powers returned to the United Kingdom government.
Although there are likely to be some tensions between the Conservatives and the DUP, the two parties have now agreed broad consensus that will give May just enough room to run a government, although nothing like the way she wanted when she called the snap election.
May hosted DUP officials for talks yesterday on an informal alliance yesterday.
The Commission has stated that one of its priorities in Brexit talks was the Good Friday Agreement, which brought an end to violence and terrorism in Northern Ireland in the late 1990s.
She will have to manage conflicting demands from within her own party, including a proposal for business groups and lawmakers from all parties to agree a national position.
The Prime Minister will attend the European Council summit to discuss issues such as migration and security, but will be absent from a dinner when the 27 other national leaders review the start of the Brexit process.
"I think we know that, the Conservative Party know that, but the specific points are open to negotiation". And he asked: "Is the populist illusion to limit free movement of people more important than the prosperity and fortune of the British workers, the British industry, the British companies and the British economy?" Data on Wednesday showed average weekly pay in the three months to April fell by 0.4 percent on the year in inflation-adjusted terms - the biggest fall since the three months to September 2014.