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Foreign Secretary Liz Truss will hold separate talks with the Democratic Unionist Party and Sinn Féin on the Northern Ireland Protocol on Monday.
Ms Truss is the UK's lead negotiator with the EU in post-Brexit talks.
The foreign secretary said she was prepared to trigger Article 16 to suspend the agreement if necessary.
The EU said it was "not too impressed" with Ms Truss' threat.
In 2019, the prime minister agreed a deal, known as the protocol, and for the last six months the UK has been attempting to renegotiate it.
The protocol is the part of the Brexit deal that prevents a hard Irish border by keeping Northern Ireland inside the EU's single market for goods.
That also creates a new Irish Sea trade border between Northern Ireland and the rest of the UK, with some goods needing to be checked as they enter Northern Ireland.
In July, the UK proposed an arrangement in which goods from Great Britain, which are due to stay in Northern Ireland, would not be checked and would have minimal paperwork.
Goods which are due to move onwards to the Republic of Ireland would be checked at Northern Ireland's ports.
The EU published its own proposals in October, which it said would significantly reduce, but not eliminate, checks on goods.
It has previously said that the easiest way to reduce checks would be for the UK to sign up to a Swiss-style agri-food agreement.
That would involve all of the UK following the relevant EU rules, something the government says it could not accept.
"I will not sign up to anything which sees the people of Northern Ireland unable to benefit from the same decisions on taxation and spending as the rest of the UK, or which still sees goods moving within our own country being subject to checks," Ms Truss said in the Sunday Telegraph.
DUP leader Sir Jeffrey Donaldson will meet Liz Truss in person in London later.
Sir Jeffrey has said his meeting with the foreign secretary will have a major bearing on his next steps.
He has threatened to pull his party out of the Stormont institutions over the issue.
Deputy First Minister Michelle O'Neill, of Sinn Féin, who will speak to Ms Truss virtually, criticised the continued DUP threats as reckless.
The EU's ambassador to the UK said it was not helpful to keep agitating the issue of triggering Article 16.
Ms Truss is due to hold two days of talks with her European Union counterpart, Maroš Šefčovič, over Thursday and Friday.
Sir Jeffrey Donaldson has already said that this meeting would have a "major bearing" on his next steps. He is a leader under pressure. The DUP is in desperate need of a life raft.
It's just about four months since Sir Jeffrey - on 9 September - first threatened to pull down the institutions within weeks unless there was a major change in the protocol.
Nothing has happened since and he's reminded of it day and daily - if not by the media, then by his political rivals within unionism like Jim Allister, the TUV leader.
The assembly election is looming unless Sir Jeffrey does something or gets something in terms of a change in the Protocol or the triggering of Article 16. That will be thrown at him and his party every day that he made a hollow threat and got nothing for it. So there's a lot riding on this meeting with Liz Truss today for Sir Jeffrey Donaldson.
Sinn Féin say they are going to remind Liz Truss that the DUP position on the protocol is not the majority one - that the majority of people here did not vote for Brexit and that her party got the hardest Brexit possible.
These are pretty polar opposite positions and you wouldn't expect anything else.
Ms Truss says that when she meets Mr Šefčovič, the EU's lead post-Brexit negotiator, she will be "putting forward our constructive proposals to resolve the situation".
It is not yet clear if these differ from the July proposals.
She has also repeated the UK's willingness to use the Article 16 mechanism of the protocol.
Article 16 sets out the process for taking unilateral "safeguard" measures if either the EU or UK concludes that the deal is leading to serious practical problems or causing diversion of trade.
Those safeguards would amount to suspending parts of the deal.
Ms Truss said: "I want a negotiated solution, but if we have to use legitimate provisions including Article 16, I am willing to do that.
"This safeguard clause was explicitly designed - and agreed to by all sides - to ease acute problems because of the sensitivity of the issues at play."
The EU has said it does not believe the use of Article 16 is justified and that its deployment could lead to the collapse of the wider Brexit deal, the Trade and Cooperation Agreement.
João Vale de Almeida, the EU's ambassador to the UK, said it was not helpful to "keep agitating the issue" of triggering Article 16.
"We've heard this before from the government, so we're not surprised. We are not too impressed," he told Sky News.
"I think we should focus on - at least that's where we are focused on - is trying to find solutions for difficulties in the implementation of the protocol".
The EU was "even more eager" to find compromises, he added.