The British government was warned against holding on to a hard border between Northern Ireland and the Republic.
Irish Foreign Minister Simon Coveney said a temporary agreement – or one that could possibly end the United Kingdom unilaterally – would never receive EU support.
The border problem is the main obstacle to progress between the two sides.
After the passage of time, Theresa May, who teaches her Cabinet on Tuesday, has to assist both the EU and its Members.
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The UK is expected to leave the EU in March, and although 95% of the deal is said to have been completed, it remains tricky to uphold the commitment of both sides not to guarantee a new hard limit in Ireland.
This is a problem because, after Brexit, it becomes the land border of the United Kingdom with the rest of the EU, which has a single market and a customs union, so that products do not need to be examined in the transition between Member States.
There were warnings that a hard line would undermine the peace process in Northern Ireland.
However, if the negotiators can not make a decisive contribution to ensuring no new visible controls, there will be no special summit to conclude Britain's exit.
Tory Brexiteers fear that the United Kingdom could end up in a tariff union with the EU without a firm end.
Former Foreign Minister Boris Johnson said in The Sun that this was an "absolute stinker" of a deal and warned against a "handover to Brussels" that would keep Britain bound by EU rules in the coming years.
However, Ms May insisted that any agreement was "strictly limited in time".
However, this is not the view of the EU.
On Twitter, Coveney said a "time-limited backstop" would "not meet the UK's past commitments."
"It is still necessary to repeat this," added Deputy EU negotiator Sabine Weyand.
However, the EU's proposal to reach an agreement specific to Northern Ireland was ruled out by Mrs May, who would undermine the integrity of the UK by creating a new border in the Irish Sea.
BBC political editor Laura Kuenssberg said Mr Coveney's comments were important because of the "deep discomfort" among the Tories to register for something without a "best before date".
The two sides will not "suddenly find a holy grail," she said – "this week must be decisive".
Lawyers call for a referendum
In the meantime, 1,400 lawyers have signed a letter in which another EU referendum will be held.
The letter's signatories include Labor colleague Baroness Kennedy QC, former Supreme Court judge Konrad Schiemann, and former European Court Justice David Edward.
They say that questions about the validity of the 2016 vote mean that it should not be the last word of the public, or the 1975 referendum on membership of the then European Economic Community.
In an earlier referendum, voters were faced with a clear choice between alternatives after the negotiations were concluded, the lawyers said.
In contrast, in the 2016 vote, "the nature of the negotiation process and its outcome was unknown," the letter said.
"Voters were faced with the choice between a known reality and an unknown alternative: in the campaign, unverifiable claims replaced facts and reality."
The UK Government has said that re-election to the public would be a betrayal of public confidence after the 2016 referendum.
A spokeswoman for the Departure from the European Union said the government was confident that they were "mutually beneficial" with the EU.
"The people of the United Kingdom have already had their say in one of the largest democratic exercises that this country has ever seen, and the Prime Minister has made it clear that there will be no second referendum," she said.