But it was later rejected by Northern Irish party DUP, which says it can not allow any divergence in regulation between Northern Ireland and other parts of the UK.
DUP sources in Belfast were the most negative, suggesting talks could "creep into January", but Whitehall officials were also very cautious about predicting any breakthrough soon.
If the agreement is not reached member states will rule that insufficient progress has been made and talks on trade and transition progress will not be able to start.
The arrangement buys time, particularly for May's government, which European Union negotiators have complained of being indecisive in what it wants amid an internal fight over the direction the country should take.
A deal fell apart on Monday when the UK's pledge of "regulatory alignment" across Ireland - to avoid border customs checks and posts - was vetoed by the DUP.
They both accepted that the border must remain open once Britain leaves the bloc in 2019, although they left it unclear how that would happen in practice. Friday's deal seems to simply delay decisions on some key points, including how to keep the Irish border open.
The UK has been handed a new deadline of Sunday to come up with a Brexit deal that can solve the border issue.
He said no particular words or combination of words were discussed.
Later in a press conference alongside Mr Rutte, he said Mrs May "wants to come back to us with some text tonight and tomorrow".
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"We will ensure that there is no hard border between Northern Ireland and the Republic of Ireland".
Ireland's prime minister, Leo Varadkar, welcomed the compromise as a step in the right direction, saying "this is not the end but it is the end of the beginning".
In a further headache for May, senior leave-supporting Tories, including the foreign secretary, Boris Johnson, are unhappy about the idea of the whole of the United Kingdom signing up to any "regulatory alignment" with the rest of the European Union, as they believe it would defeat the point of Brexit. Farage tweeted that the deal was "good news for Mrs".
Speaking on RTÉ's Morning Ireland, Mr Grant said unless Britain stays in the customs union and the single market, there will have to be border controls between the United Kingdom and the EU. "The [government and DUP] teams in London are continuing to work through the detail".
Already, precious time has been lost.
European Council President Donald Tusk, who will chair next Thursday's summit, grimly pointed out that 18 months have passed since Britain voted to leave the EU, yet the hardest work must still be done.
In a letter to the prime minister, the MPs, including former cabinet ministers Nicky Morgan, Ken Clarke and Stephen Crabb, said: "We are disappointed that, yet again, some MPs and others seek to impose their own conditions on these negotiations".
"That's the bit where we will achieve a new trading relationship with our friends and partners".