Arlene Foster has said talks with Theresa May have been "useful".
The DUP leader met with the Prime Minister in Downing Street on Thursday morning, as efforts to break the parliamentary deadlock over Brexit continue.
Ms Foster said her party's issue remains "the backstop" and said she wants a withdrawal agreement that works for the whole of the UK and the EU.
Speaking outside Downing Street after meeting Mrs May, she said: "Our problem with the backstop is of course that it separates Northern Ireland out from the rest of the UK in terms of market regulation and in terms of the customs union."
Her deputy Nigel Dodds said: "[The Prime Minister] has a way through this and the problem for a lot of her own backbenchers and of course for us has been the backstop.
"If she can address that issue in a satisfactory way and if the EU realise this is the issue holding up the withdrawal agreement then we can make progress."
He said the details on how progress could be made are being discussed but that it was not "useful to give too much of a running comment on the details of that".
Mr Dodds said there were "a lot of good engagements going on and we'll continue to work at it".