Northern Ireland has been without a devolved government for almost two years after the DUP walked out in protest over the trade rules, which it says has created barriers with the rest of the United Kingdom and undermined Northern Ireland's place in the union.
Jeffrey Donaldson said a meeting of senior DUP lawmakers last Friday was "not a make or break meeting" and that talks with London would continue.
"To date no agreement has been reached and there remains a number of important issues that have to be finalised if we are to see a restored assembly," Donaldson said in a video posted by the Cool FM radio station.
"We are of the view that given the progress that has been further secured, we will endeavour now to close the remaining gaps between us."
Irish nationalists and pro-British unionist politicians are obliged to share power under the terms of the 1998 Good Friday peace accord that ended three decades of sectarian violence in Northern Ireland.
With budget pressures mounting, the British government in December said it would provide Northern Ireland with 3.3 billion pounds ($4.2 billion) of additional funding over five years but only if an agreement is reached to re-establish power-sharing.
(Reporting by Padraic Halpin; editing by William James)
