The five main Stormont parties have held roundtable talks with the British and Irish governments amid the crisis in the health sector.
They discussed efforts to restore power-sharing and a health summit to be convened on Thursday.
On Tuesday night, party leaders asked the secretary of state to take control of the issue.
However, Julian Smith insisted it is a devolved matter.
Representatives from the Stormont parties met Mr Smith and tánaiste (Irish deputy PM) Simon Coveney on Wednesday afternoon.
Speaking after the meeting, which also covered an Irish Language Act and the Petition of Concern, DUP MLA Edwin Poots said there was an “existing goodwill” from the parties involved in talks to restore power sharing, and that the issues could in theory be dealt with in the next few weeks.
“Let us build on that goodwill. The differences are on the margins, the key issue for us is health,” he said.
The former health minister added that he believed Julian Smith was right not to intervene in the pay dispute, arguing it was ultimately a Stormont problem and one the parties should resolve themselves.
He also said he did not detect, on Sinn Féin’s part, that they were willing to go back into the executive now to resolve health, and deal with the other issues in a parallel talks process.
In a statement, Sinn Féin vice president Michelle O’Neill accused Mr Smith of “exploiting the suffering of patients as political leverage in the talks”.
Mrs O’Neill said the secretary of state was refusing to resolve the dispute “in order to exert pressure on party leaders”.
“I told him he could and should immediately resolve the pay issue,” she said.
“A solution is available which would end the dispute, but the British secretary of state is holding back on this in a cynical attempt to pressurise the political parties.”
Tweeting after the meeting Mr Smith said he was “deeply concerned by the health crisis” and that the Stormont parties must address it as an “immediate priority”.
Ulster Unionist leader Steve Aiken said parties had told the secretary of state they were “disappointed” he had chosen not to back them on their call for him to intervene directly and resolve pay parity.
On the restoration of the assembly, Mr Aiken said the political parties needed to do a deal “for the sake of our health workers and public service workers”.
“We do need to get an agreement and we do need to move on,” he said.
“It’s taken three years to get to this point. The political leadership of this country needs to sit down and take responsibility.”
The BBC understands the health summit will aim to ensure that if devolved government is restored, it will be able to resolve the healthcare issues.