Theresa May will try to reassure people in Northern Ireland that she can secure a Brexit deal that avoids a hard border with Ireland during a visit later.
In a speech to business leaders, the prime minister will pledge to secure a deal with the EU that “commands broad support” and a majority in parliament.
The DUP leader Arlene Foster said the “toxic backstop” remains the problem.
In Westminster, the working group of Leave and Remain MPs will continue to try to agree alternative solutions.
However, European Union leaders have continued to rule out making changes to the withdrawal deal as agreed.
The prime minister is expected to say in her speech that she will find a way to deliver Brexit that honours “commitments to Northern Ireland” and “secures a majority” in parliament.
The backstop is an insurance policy designed to avoid a hard border “under all circumstances” between Northern Ireland and the Irish Republic after Brexit.
The UK is due to leave the EU at 23:00 GMT on Friday 29 March, when the two-year time limit on withdrawal negotiations enforced by the Article 50 process expires.
Mrs Foster said Parliament had spoken and the current backstop has been rejected.
“The European Union must now accept the need for the withdrawal agreement to be reopened,” she added.
The BBC’s Brussels reporter Adam Fleming said the EU was not looking for a substitute solution, because it says it has already investigated every other option that exists and none has the same effect as the backstop.
The EU’s chief negotiator, Michel Barnier, said there was “full agreement” that the withdrawal agreement “cannot be reopened”.
On Monday, German Chancellor Angela Merkel said the EU would listen to proposals to solve the Irish border “riddle”, although they needed to hear how the UK wanted to do it.
Tánaiste (Irish deputy prime minister) Simon Coveney said the withdrawal agreement rejected by MPs already allowed the EU and UK to work on alternative arrangements for the backstop.
“What Ireland is being asked to do by some in Westminster is to essentially do away with an agreed solution between the UK government and EU negotiators and to replace it with wishful thinking and I think that’s a very unreasonable request to ask the Irish government to be flexible on,” he added.
In January, MPs overwhelmingly rejected the withdrawal deal that the government had negotiated with the EU.
Last week, they voted for the prime minister to seek “alternative arrangements” to the controversial Irish “backstop” proposal, which is opposed by many Conservative MPs and the Democratic Unionist Party.
If used, the backstop would effectively keep the UK inside the EU’s customs union, but with Northern Ireland also conforming to some rules of the single market.
Critics fear the UK could be “trapped” in this arrangement for years, while Unionist MPs in Northern Ireland also fear it would divide Northern Ireland from the rest of the UK.
The first meeting of the Alternative Arrangements Working Group on Monday was described as “detailed and constructive” by the Brexit department.
While in Northern Ireland, Mrs May will also call for “steps to move towards the restoration of devolution” so that Northern Ireland’s politicians “can get back to work on the issues that matter to the people they represent”.
Mrs May will say: “The measure of this moment in Northern Ireland’s history must be more than whether we avoid a return to the challenges of the past.
“It must be how, together, we move forwards to shape the opportunities of the future.”