She hosted DUP leader Arlene Foster at Downing Street to thrash out the terms of the Northern Ireland party's backing and agreement to vote with the Tories on policies in the House of Commons to get bills through.
"Discussions are going well with the government and we hope soon to be able to bring this work to a successful conclusion," Foster said in a tweet after meeting May.
Sir Majortold BBC Radio 4's World at One that if the Conservatives "locked" themselves into a deal with one of the main parties in Northern Ireland, there was a danger the government would no longer be seen as an "impartial honest broker" in restoring the power-sharing arrangements and upholding NI institutions.
He suggested the DUP would be asking for money and that would be seen as the "government paying cash for votes in parliament", and would be received badly in other parts of the UK.
The DUP is expected to make a better economic deal for Northern Ireland the central factor for any deal, officially referred to asa "confidence and supply deal".
"We enter these talks in a positive fashion, we are first and foremost unionists and therefore we want to secure the union. Butwe are going into these talks with the national interest at heart," Foster had said ahead of the meeting.
Soon after the meeting, May set off to the House of Commons where MPs were reconvening for the first time after the June 8 general election and overwhelmingly re-elected John Bercow as the Speaker of the House.
Addressing a packed House, she urged MPs to "come together in a spirit of national unity" to tackle the challenges facing the UK, urging them to help the country overcome divisions between "old and young and rich and poor".
Opposition Labour leader Jeremy Corbyn congratulated May on "returning as PM" and said he "looked forward to this parliament, however short it may be", in reference to her weakened support base as the head of a minority government.
Yesterday, May had faced the tough 1922 Committee of her party's backbench MPs amid a brewing rebellion within the ranks after her gamble to call a snap general election backfired, leaving the Tories eight seats short of a majority.
"I got us into this mess, and I'm going to get us out of it," May told her party MPs.
The British prime minister is set to travel to Paris to hold talks with French President Emmanuel Macron after the meetings today. They will announce joint plans to fine social media companies such as Facebook, Twitter and Google if they fail to remove extremist content from their websites.
The two leaders will hold their bilateral dialogue as they attend a France vs England international friendly football match.
May hopes to make an ally of Macron before the formal opening of Brexit negotiations, which is expected to take place next week.
The Brexit negotiations with the European Union were set to kick off yesterday, but have now been delayed until later next week.
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