Sir Jeffrey Donaldson has said he "flatly rejects" that the DUP is to blame for talks to restore devolution failing to reach agreement.
On Thursday, the British and Irish governments said progress had been made, but laid the blame at the feet of the DUP for the lack of a deal.
Sir Jeffrey said the DUP had more talks with the secretary of state on Friday morning.
Sinn Féin leader Mary Lou McDonald said no single party should block a deal.
However, Sir Jeffrey said his party "is not an impediment to progress here".
"Our priority now is to get Stormont back up and running so that we can tackle the issues related to the crisis in the health service," he added.
However, he said no text for a proposed deal had been presented to the parties.
"We want to see in black and white what is proposed here in terms of the outstanding issues," he said.
"How can we agree to something we haven't seen."
Sir Jeffrey said that DUP ministers were ready to be appointed "from day one", but added that any deal had to be balanced and fair.
On Thursday, NI secretary Julian Smith said he was "deeply disappointed" that all the parties were not yet in agreement.
Irish Tánaiste (Deputy Prime Minister) Simon Coveney said a deal could still be reached if the DUP changed its approach.
On Friday, Sinn Féin's Ms McDonald said that "we have a process of negotiation and engagement and the DUP have put the brakes on it".
"We're ready to do the business, and so now the challenge falls to others and to the DUP in particular," she added.
"None of us on the brow of Christmas want to have an argument or altercation with the DUP, we want to get the business done, we want to get good government done for everybody here in the north.
"That's the challenge, we have no interest in a blame game."
She said either an agreement was concluded "or we go to elections".
The SDLP's Nichola Mallon said she was "struggling to understand why the DUP need more time".
"We either do it the week before Christmas or we do it the week after," she said.
Northern Ireland has been without devolved government since January 2017.
The NI Assembly collapsed when the two biggest parties - the Democratic Unionist Party (DUP) and Sinn Féin - split in a bitter row over the DUP's handling of a green energy scandal.
It is unclear whether talks will resume before Christmas.
The governments say devolution must be restored by 13 January 2020, or the Northern Ireland secretary will call a fresh assembly election.
Parties should reflect
Speaking after a meeting involving the five main parties and the tánaiste, Mr Smith said they were "very close to being able to table a text of agreement and compromise".
"I believe if we could table a text we could be back in the assembly on Monday.
"But unfortunately we do not have all parties on board, so the judgement I have made is that we should not table text.
"We will allow all parties to reflect on the impact of that decision on people in Northern Ireland who are deeply affected by the lack of decision making at Stormont."
Had been told earlier today by a Stormont source that the DUP was “dragging its feet” over reform of the petition of concern.. the parties tonight were unwilling to single out one issue as the stumbling block but clear roundtable an attempt to bounce the DUP into moving on a deal— Jayne McCormack (@BBCJayneMcC) December 19, 2019
Mr Coveney said if there was a change of approach from the DUP, a deal could still be reached before Christmas.
But he warned the governments would not bring parties back on Friday to "waste their time".
What's the DUP's stumbling block?
What an unusual move by the two governments - calling out the DUP for stopping a Christmas breakthrough.
While talks have been ramping up at pace this week, one Stormont source said the DUP was "dragging its feet" over reform of the petition of concern.
It's not clear what exactly the stumbling block regarding the use of the controversial veto mechanism is, but Thursday's roundtable seemed to be an attempt to push the DUP over the line.
But already the DUP has reacted badly to the governments' tactic, saying it won't be bounced into anything and insisting there cannot be deadlines on such a sensitive process.
Given the current deadline is next month, things might pause over Christmas and allow the parties more time to assess their positions.
Come January though, there are only two choices left - take the deal on offer or face a fresh election.
Some in the DUP will find neither of those options appealing.
If a petition of concern is presented to the assembly speaker, any motion or amendment will need cross-community support.
Effectively this means that, provided enough MLAs from a particular community agree, that community can exercise a veto over the assembly's decisions.
'Have courage and lead'
Alliance Party leader Naomi Long described it as a "disappointing end" to the week, and said the parties needed to come back after Christmas and get a deal over the line.
"I believe a deal could be done now, real progress has been made - unfortunately not all of the parties agree that is the case," she said.
"People now need to have the courage and lead, rather than simply wait for others."
Ulster Unionist leader Steve Aiken said his party would be ready with their "phones on" over Christmas to restore devolution.
"It would be interesting if we knew what the DUP's legitimate concerns were," he said.