Negotiations over the UK's EU reform demands are at a "critical moment" and the risk of break-up "is real", EU Council president Donald Tusk has said.
Mr Tusk, who is overseeing the negotiation, urged European leaders to handle the situation "with care".
UK PM David Cameron is seeking a deal at this week's crunch EU summit before holding the UK's referendum.
Earlier he bowed to pressure to hold a cabinet meeting straight after the summit if a deal is agreed.
A Number 10 spokesman said the prime minister and French President Francois Hollande had held "constructive discussions" on the UK renegotiation when they met in Paris late on Monday.
"They agreed that we are making good progress... and that the draft text from the European Council provides a firm basis to reach agreement at this week's summit," the spokesman said.
Mr Tusk is on a tour of European countries ahead of the two-day summit of EU leaders, which begins on Thursday.
Speaking after holding talks with the Romanian and French presidents, he said negotiations on Britain's future inside the 28-member bloc were "difficult but… hugely important".
Reflecting on the talks, he said: "This is a critical moment. It is high time we started listening to each other's arguments more than to our own.
"It is natural in negotiations that positions harden, as we get closer to crunch time.
"But the risk of break-up is real because this process is indeed very fragile. Handle with care. What is broken cannot be mended."
BBC assistant political editor Norman Smith said Mr Tusk was trying to "concentrate minds" ahead of the EU summit as leaders of the different member states stake out their positions.
The French government is said to be concerned about UK calls for protection for non-eurozone countries, but No 10 said the French had shown "willingness" to find a solution.
As part of his diplomatic push, Mr Cameron - who met German Chancellor Angela Merkel for talks on Friday - will discuss the renegotiation with European Commission President Jean-Claude Juncker on Tuesday, as well as senior MEPs.
If a deal is agreed on the PM's reforms, which also include curbs on migrants' welfare entitlement, he will hold a cabinet meeting on Friday evening, sources have told the BBC.
Downing Street has said ministers cannot speak out until the cabinet has met to agree a government position, and it was claimed this would give the Remain campaign an unfair head start if a meeting was delayed until the following week.
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