Theresa May has held telephone talks with DUP leader Arlene Foster in an attempt to break the Brexit deadlock over the Irish border issue.
May is calling on the party to support proposals that would allow the EU to trigger the next stage of trade negotiations.
On Monday (December 4) May's bid to do a deal with the EU over the Irish border was scuppered by the DUP, who refused to accept wording regarding "regulatory alignment" across the border which they suggested would create an effective customs divide in the Irish Sea.
The Prime Minister is hoping to get the DUP on board ahead of a key EU summit on December 14, which will decide whether trade talks can finally begin.
The call was scheduled for yesterday (December 5) however, in a possible sign of how intractable the issue has become, the call did not take place.
Foster has complained that her party was only shown the proposed text regarding the Irish border late on Monday morning, around the time the Prime Minister was sitting down to lunch in Brussels with European Commission president Jean-Claude Juncker.
Dublin has warned that unless the UK provides cast-iron guarantees that the border will remain open, it will not allow the Brexit talks to expand to trade relations.
Reports have also suggested the Cabinet have voiced unease about May's signing the UK up to any deal which would stop it diverging from EU regulations on issues like food safety, environmental protection and workplace rights after Brexit.
Boris Johnson has told reporters outside a Nato summit in Brussels: "We will come up with a solution, but the important thing is that that solution can only be discovered in the context of discussions on the end-state of the UK's relations with the rest of the EU.
"We need to get on with those negotiations now, so all the more reason to get on with stage two of the negotiations."
The foreign secretary added: "What I would say is that the best way to sort it out is to get on to the second phase of the negotiations, where all these difficult issues can be properly teased out, thrashed out and solved."