However DUP leader Arlene Foster refused to accept any terms which would see Northern Ireland leave the EU on different terms to the rest of the UK after Mrs May proposed aligning the state with the Republic.
The PM has now cleared her schedule for crunch talks in Westminster, as well as with leaders in Brussels and on both sides of the Irish border.
Next week Mrs May will put forward her final offer to the EU before the December summit on Thursday and Friday.
A deal will need to be in place with Dublin and Stormont by the end of this week, however, with Mrs May expected to return to Brussels on Friday.
With little work expected over the weekend – especially given the DUP’s refusal to carry out talks on Sundays due to their religious reliefs – the next four days will be crucial.
Mrs May could return to Brussels as soon as tommorrow as the clock keeps ticking on Britain’s Brexit countdown.
Check back throughout the day for live updates below as Mrs May fights to save Brexit.
Theresa May has four days to come to a Brexit agreement
1.25pm – DUP warns Anglo-Irish relations suffering
Anglo-Irish relations have been set back by the Irish government’s “aggressive and anti-unionist” approach in Brexit talks, the DUP has claimed.
Nigel Dodds, the DUP’s Westminster leader, warned relationships in Northern Ireland linked to devolution have also been damaged and said they will “take a long time to repair”.
Mr Dodds added his party’s approach of seeking to “stand strong for the Union” and Northern Ireland’s place within it should come as no surprise.
1.02pm – Jacob Rees-Mogg thanks DUP
Jacob Rees-Mogg asks whether Downing Street would like to join him in thanking the DUP.
He said the unionist party helped the Tories stick to their own red lines”.
He asked: “Does my right honourable friend share my gratitude to the DUP for helping the government stick to its own red lines.”
12.55pm – David Davis speak out
David Davis says in response to the urgent question “no paet of the UK will be left in the customs union” after Brexit.
He said progress is being made and a deal is close.
However he suggests the Irish border is best dealt with in stage two of talks.
12.42pm – Urgent question begins
Mr Starmer begins his urgent question by exclaiming: “What an embarassment.
“The DUP tail…