The DUP leader has said he "hopeful" agreement can be reached between the UK government and EU over the Northern Ireland Protocol which meets his party's demands.
Sir Jeffrey Donaldson was speaking to reporters in Belfast after a lengthy meeting with the Prime Minister on Friday.
Rishi Sunak made a short trip to Northern Ireland and updated all Stormont parties on the current negotiations with the EU.
Sinn Féin's President Mary Lou McDonald also welcomed "significant progress" in relation to the ongoing Protocol negotiations, adding that her party wants a "speedy conclusion of matters".
The Prime Minister's visit comes amid mounting speculation that a deal between the EU and UK could be unveiled early next week.
Following his visit to Northern Ireland, Mr Sunak is set to join European leaders in Germany this weekend for the Munich Security Conference and the protocol is likely to feature in discussions on the margins.
Power-sharing institutions have not be restored in Northern Ireland since 2022. The DUP removed its first minister from Stormont's executive due to its concerns over the Northern Ireland Protocol.
The post-Brexit trade deal has resulted in checks being carried out on some goods coming into NI from GB. The DUP outlined seven tests which it said any potential protocol resolution would need to meet before it would consider re-entering the power-sharing institutions. After meeting with the Prime Minister on Friday, Sir Jeffrey Donaldson said: "I think that progress has been made across a range of issues and we welcome that but I think there are still some issues where final agreement with the EU is still outstanding. We hope that that agreement can be reached."
He explained that the DUP has not yet seen the final text of any agreement.
"We want to see the final text of any agreement so that we can make our judgement calls, we can assess any agreement against our seven tests and come to a decision as to whether that agreement meets those tests and provides the basis for restoring devolution in Northern Ireland based upon the restoration of Northern Ireland's place in the United Kingdom and its internal market."
Sir Jeffrey continued: "The decisions that will be taken by the Prime Minister and the European Commission will either consign Northern Ireland to move division or they will clear a path towards healing and the restoration of the political institutions.
"I have indicated to the Prime Minister that it is important, fundamentally important, that he agrees the right deal.
"I want to hear the Brussels will stretch itself to recognise the concerns that we have as unionists and that this process will correct the wrongs of the last negotiations I do not believe anyone should be led by a calendar.
"What is fundamentally and most important here is getting it right, that must be the ultimate goal, that is our goal, that is what we are committed to."
Meanwhile after meeting with the Prime Minister, Sinn Féin's President said: "It is clear now that significant progress has been made and we're very heartened by that."
"We now want to see a speedy conclusion of matters and above all else we want to see the institutions restored, government restored, here in the north," added Mary Lou McDonald.
"The bottom line is that we have to ensure that any deal provides for ongoing access to the European Single Market, no hardening of the border on the island of Ireland and a protection of the Good Froday Agreement in all of its parts, those are the core elements and aspects that need to be protected."
Meanwhile SDLP Leader Colum Eastwood said he believed Mr Sunak was "ticking the box" of engaging with the Stormont parties.
"I think he's very careful not to get into too much detail until the deal is done and I suppose that's fair enough," he said.Alliance Leader Naomi Long said that she explained to the Prime Minister the importance of dual-market access for Northern Ireland.
"We were trying to convey to him the importance to local businesses, and to Northern Ireland as a whole, of having a relationship with the EU that is positive and constructive, of having stability, of maintaining dual access in terms of markets, and on us being able to move forward and restore the Assembly," she told reporters.
Ulster Unionist leader Doug Beattie claimed that the details on a potential deal were not outlined during his meeting with Mr Sunak.
"We are in that position where we could have something next week, but it may be another couple of weeks yet," he said on the prospects of an agreement.
"We don't know and I don't leave here knowing much more than I knew when we first went in. But certainly the Prime Minister was enthusiastic, engaged and positive, and that has has given me something to take away from this."
Want a quick and expert briefing on the biggest news stories? Listen to our latest podcasts to find out What You Need To Know.