Sinn Fein, which won seven seats in the British parliament last week but does not take up its seats or vote in Westminster, would likely reject a deal to form a government by refusing to work with the DUP in Northern Ireland.
It had been hoped May and DUP leader Arlene Foster would reach an agreement Wednesday that would give the Conservatives a small working majority.
The announcement of any agreement is set to be delayed because of the tragic fire in a London tower block.
The two leaders also discussed the fight against terror, and said they would launch an Anglo- French campaign to help firms clamp down on online hate speech. "An agreement to restore devolved power-sharing government in Stormont must be reached by the 29 June deadline", he said.
"Northern Ireland's political leaders now have it in their hands to take control and shape a brighter future for everyone in Northern Ireland".
Theresa May's failure to win a majority at the General Election has led to suggestions her Brexit plan to leave the EU's Single Market and Customs Union could be altered, while rival parties have demanded involvement in exit talks following the inconclusive result.
The proposed deal would see the DUP back the Conservatives in votes on the Budget and on any confidence motion while other matters would be negotiated on an issue-by-issue basis.More news: GE's Immelt to retire, John Flannery to take over as CEO
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Brexit Secretary David Davis and the European Commission's chief negotiator Michel Barnier agreed during discussions in Brussels on Thursday to start formal talks over the UK's departure on 19 June.
The EU's chief Brexit negotiator, Michael Barnier and the UK's Brexit minister, David Davis, will meet in Brussels on Monday (19 June), kicking off negotiations likely to take nearly two years.
"It's going to be hard".
The Times reported that Chancellor Philip Hammond was preparing to fight for the United Kingdom to remain within the EU's customs union.
Philip Hammond, Britain's finance minister, says protecting the British economy should be the main objective of upcoming negotiations over the country's exit from the European Union.
"It's a unity of objective, having voted to leave the European Union, that their government gets on with that and makes a success of it".
"There is a unity of objective among people in the United Kingdom", May said following a meeting with French President Emmanuel Macron in Paris.