Alliance Party leader Naomi Long said patience at Westminster for talks to restore devolution had “almost expired”.
She said the 23-month crisis should end “for the sake of the people we represent.”
Northern Ireland Secretary Chris Heaton-Harris is holding talks with the parties in Hillsborough.
Mr Long accused the Democratic Unionist Party (DUP) of holding democracy “to ransom”.
The DUP withdrew from the executive branch in February 2022 in protest at a post-Brexit trade deal for Northern Ireland.
After speaking with the Secretary of State, DUP leader Sir Geoffrey Donaldson said “significant progress” had been made on the issue.
But he said there was still a funding gap in Northern Ireland that the UK government needed to address.
Ms Long told reporters she would “appeal” to the DUP to return to Stormont as public services were “creaking” under the current pressures.
“Please step up to the plate.”
Sinn Féin deputy leader Michelle O’Neill said the party was not in a positive mood after the meeting.
“There was nothing that gave us a glimmer of light, if you want to put it that way,” O’Neill said.
“Having said that, we think there is still an opportunity for the DUP to act proactively.
Monday’s meeting follows a roundtable discussion between the parties and the Northern Ireland Secretary in December.
Mr Heaton-Harris said if Stormont’s executive was not back by Friday, several decisions would have to be made, including enacting the Primary Bill in Westminster next week.
He added that talks with the DUP on post-Brexit trade provisions, the Windsor Framework, had effectively concluded, but there had been “further progress in the last week”.
He said funding for the refurbished Stormont had been “very generous” but public sector pay had been devolved.
Michelle O’Neill said on Monday: “We have told the Secretary of State that he has made the funding available so he should go ahead and pay the workers.”
protesters outside the venue
Members of all five of Northern Ireland’s education unions protested outside the castle gates.
As the ministers arrived, autism support groups also staged a protest outside the meeting venue.
They spoke on behalf of families affected by the closure of special schools during this week’s strike and shouted at the DUP: “You’re on the payroll, pay them.”
The DUP delegation, made up of Sir Geoffrey, Gavin Robinson and Emma Little-Pengery, arrived in Hillsborough following shouts from protesters.
Some chanted “fair pay for teachers,” while one protester yelled “shame, shame, shame.”
“We discussed the significant progress made in negotiations with the Government on the issues raised by the Northern Ireland Protocol and the need to build on progress made under the Windsor Framework,” Sir Jeffrey said.
“I think we’re moving toward a moment where we can make decisions about how we move forward on all of these issues.”
The DUP leader added that regardless of whether a resolution to restart Stormont was found, the money must be released into public sector salaries.
“Stormont does not need to be functioning for the secretary to use the temporary powers granted to him for that purpose.
“He has the authority to set the budget and address this issue, so he should go for it,” he added.
Why did Stormont fall?
Northern Ireland’s devolved government collapsed in February 2022 after the Democratic Unionist Party (DUP) left in protest of post-Brexit trade checks between the region and the UK.
It believes that an agreement under the Northern Ireland Protocol would reduce the region’s position in the UK domestic market.
A new agreement, known as the Windsor Framework, has been agreed between the UK government and the European Union in 2023, aimed at addressing concerns.
But the DUP says this is not enough and the party has been in talks with the government for several months seeking further reforms.
Mr Heaton-Harris said in December that these talks were “effectively over” and proposed a £3.3bn financial package for Northern Ireland, conditional on Stormont’s institutions being restored.
Is the NI Director under pressure?
I had little hope that anything would change, but as far as I was concerned, I was not disappointed.
There are still people pleading with the DUP to end the boycott by Thursday, but it seems unlikely that will happen.
One union member told Geoffrey Donaldson that he should return to Stormont now. In response, Jeffrey Donaldson said, you have the power to strike action, but we have the power to not participate until we get the progress we want.
Thursday is the deadline by which Chris Heaton-Harris must call an election unless devolution is restored. We’re sure he wouldn’t do that. He is likely to extend the deadline, but for how long will he extend it? I do not understand.
It’s hard to tell if Chris Heaton-Harris is under that much pressure.
‘Twilight Zone’
Doug Beatty, leader of the Ulster Unionist Party, said there had been “no movement of any note” in recent talks with the Northern Ireland Secretary.
“2023 ended without a deal because nothing changed. 2024 started without a deal.”
Mr Beatty said he expected the basic legislation to set Northern Ireland’s future governance structure to be enacted at Westminster next week.
Social Democrat and Labor Party leader Colum Eastwood said Stormont politics were in a “twilight zone” after his meeting with Heaton-Harris on Monday.
“I’ve heard that they have come close many times over the past two years.”
He added: “I think it’s a scandalous act at this point.”
What happens after Thursday?
The industrial action also coincides with the legal deadline for restoring Stormont’s electricity share.
If the Executive is not formed by Thursday, the Northern Ireland Secretary will be legally obliged to call early parliamentary elections.
However, Heaton-Harris has postponed this deadline several times in the past and has indicated it may be postponed again.
He previously said he was “carefully considering all options” but was “not treating this date as a goal.”