The EU's Brexit negotiator Michel Barnier said ahead of a meeting of EU ministers that the main challenge now is to turn British proposals on the complex issue of the border on the island of Ireland into something binding.
Barnier said it is "high time to turn good intentions into a legal text."
Dutch Foreign Minister Stef Blok said the British proposals to keep the Irish border protected from smuggling and fraud once the U.K. leaves the bloc remain insufficient.
"The U.K. proposal contained some steps forward but not enough to guarantee that the internal market will be protected," Blok said.
EU leaders are meeting for a two-day summit in Brussels from Thursday. Brexit will top the agenda as the Oct. 31 Brexit deadline looms.
"Even if an agreement will be difficult — more and more difficult, we think — it is still possible this week," Barnier said.
EU ministers insisted it was for Prime Minister Boris Johnson to make the next move, with French Europe Minister Amelie de Montchalin saying that the EU nations "will be firm on our fundamentals."
Meanwhile, the insistence that the summit this week would be a cutoff moment is quickly fading.
Three EU nations have predicted the negotiations could spill over into next week.
Antti Rinne, prime minister of Finland, which currently holds the rotating EU presidency, said in Helsinki late Monday that he had given up hope for a quick breakthrough ahead of the Brexit summit.
"There is no time in a practical way, and in legal base, to reach an agreement before the meeting," Rinne said. "We need to have more time."
Blok agreed. "Let's use the remaining time until the Oct. 31." There has been increasing talk about an extra summit close to the end of the month.
Technical teams from Britain and the EU worked through the weekend and Monday, but both sides said significant gaps remained between their positions.