The European Union will not accept Britain's Brexit offer if Ireland is not satisfied with proposals for future border arrangements, EU President Donald Tusk said in Dublin on Friday.

Tusk spoke after meeting Ireland Prime Minister Leo Varadkar ahead of a Monday deadline by which the EU wants to hear British proposals on sticking points if Brexit talks are to advance.

The EU chief backed Ireland's demands for British guarantees that there will be no hard border between Ireland and British-controlled Northern Ireland after Brexit, which might upset the fragile peace in the region.

"If the UK offer is unacceptable for Ireland, it will also be unacceptable for the EU," Tusk said at a joint press conference with Varadkar.

"I realise that for some British politicians, this may be hard to understand but such is the logic behind the fact that Ireland is the EU member while the UK is leaving.

"This is why the key to the UK's future lies -- in some ways -- in Dublin," he added.

All sides agree there should be no return to physical border checks after Brexit, but Dublin's demand for written guarantees from Britain has proved an obstacle to an early agreement, threatening to delay the wider negotiations and causing tensions with London.

Varadkar said there had been "some progress" on border talks, but warned Britain: "I'm prepared to stand firm with our partners if needs be if the UK offer falls short."

Dublin wants "reassurance" that regulations on issues such as food safety and animal welfare would be maintained in Northern Ireland, to avoid damaging cross-border trade once Britain leaves the EU's single market and customs union.

"We can't be asked here to leap into the dark by opening up a phase two discussion in the hope that these issues might be resolved," Coveney told BBC radio.

Britain insists the issue of the Irish border can only be resolved as part of negotiations on its future partnership with the EU.

Tusk appeared to acknowledge the point, saying: "It is clear that we cannot reach a full agreement on every single detail at this stage, especially that the final outcome will be linked to the future relations between the EU and the UK."

- Ireland should 'wind its neck in' -

A British newspaper reported on Thursday that the two sides were close to a deal that would avoid regulatory divergence between Ireland and Northern Ireland, even if the rest of Britain moved away from EU rules.

The Times said this would involve devolving powers to the assembly in Belfast to allow them to keep similar customs arrangements to Ireland on agriculture and energy.

But the pro-British Democratic Unionist Party (DUP), the largest in Northern Ireland, reacted angrily to any suggestion of creating separate rules for the province.

It warned that agreement on those terms would threaten its support for British Prime Minister Theresa May's Conservatives, which keeps her minority government in power.

"If there is any hint that in order to placate Dublin and the EU, they're prepared to have Northern Ireland treated differently than the rest of the UK, then they can't rely on our vote," DUP lawmaker Sammy Wilson told the BBC.

Former Northern Ireland first minister Peter Robinson, a former leader of the DUP, called on Dublin late Thursday to stop interfering, saying: "In layman's terms, the South needs to wind its neck in."

- Brexit cannot destroy peace -

The British government says negotiations are continuing with Ireland, but its proposals for a solution were savaged on Friday by a committee of MPs, who warned that a "hard border" in Ireland seemed inevitable.

This has raised fears that the Good Friday Agreement, the peace deal that erased the border and ended generations of conflict in Northern Ireland that killed 3,500 people, could be under threat.

"We cannot allow Brexit to destroy this achievement," Tusk warned Friday.

EU leaders meeting in Brussels on December 14 and 15 will decide if there has been "sufficient progress" on the Irish border, Britain's financial settlement and EU citizens' rights to move on to trade talks.

A deal is close on the latter issues, but failure to make headway on Ireland would deal a major blow to Britain's hopes of agreeing a new trade deal with Brussels before it leaves the EU in March 2019.