A future programme for government and a budget were discussed by the parties, which are entitled to nominate ministers following last month’s Assembly election.
The post-Brexit trade arrangements have been opposed by unionists as a border in the Irish Sea.
While ministers remain in place in a caretaker role, they cannot take new decisions.
DUP leader Sir Jeffrey Donaldson met with a number of Westminster politicians on Tuesday, including Labour leader Sir Keir Starmer, to emphasise the need for action over the protocol.
The parties met this morning with the head of the civil service. We were discussing the need to agree a programme for government, agree a budget, agree a work plan for the year ahead
Sinn Fein Stormont leader Michelle O'Neill
A LucidTalk poll in Tuesday’s Belfast Telegraph found that three-quarters of unionist voters believe the DUP should not return to government at Stormont until there are at least “significant changes” to the protocol.
Further detail on proposed legislation which may override sections of the protocol is expected to emerge later this week.
Sinn Fein Stormont leader Michelle O’Neill said she regrets that, five weeks after the Assembly election, the DUP is “still boycotting” the Executive.
She said issues with the protocol can be “worked on in tandem” with talks on smoothing the protocol while the Stormont Executive functions and urged the DUP to nominate ministers.
“The parties met this morning with the head of the civil service. We were discussing the need to agree a programme for government, agree a budget, agree a work plan for the year ahead,” she told media at Belfast City Hall.
“You only can take those things so far, of course, because we do not have a functioning Assembly and an Executive.
“I regret that, that we’re five weeks post election where the people voted for parties to work together and here we are today, where the DUP are still boycotting the formation of an Executive which would allow us to actually respond to the things that really troubling people right now, the cost of living crisis, the things that are really worrying people about the difficult months that we have ahead.
“So even at this stage I still again today call on the DUP to join the rest of the parties who actually want to agree a programme for government, agree a budget, prioritise our health service, prioritise putting money in people’s pockets.
“Because even as we speak today, whilst there has been announcements from Treasury over the course of recent weeks, we still don’t know, and Conor as our Finance Minister, still doesn’t know how that money is actually going to get into people’s pockets because we do not have an Executive.
“I don’t think that’s a tolerable situation and I encourage the DUP to join with the rest of us and make politics work.”
Ms O’Neill welcomed an announcement by DUP Education Minister Michelle O’Neill of grants for families of children entitled to free school meals over the summer months.
However she said the move is “no substitute for having a fully functioning Assembly and Executive”.
“We should not spend any energy trying to find workarounds or trying to push the boundaries of ministerial responsibility. What we should have is fully functioning ministers in post around an Executive table,” she said.
Sir Jeffrey said: “Real progress is only made in Northern Ireland when there is consensus, yet the protocol was foisted upon the people of Northern Ireland despite every unionist MLA and MP opposing it.
“It was madness to press ahead and ignore the unionist opposition.
“Unlike Westminster, we operate powersharing in Northern Ireland, not majority rule.
“Not one unionist MLA supports the protocol. That represents more than 40% of the votes cast at the recent election.”
He added: “The protocol must be replaced by arrangements that restore our place within the United Kingdom and the new arrangements must command the support of unionists as well as nationalists.
“I have urged people across Parliament to recognise the seriousness of this matter and resist the temptation to play politics with Northern Ireland.
“The protocol threatens our place in the United Kingdom, endangers jobs for our people, drives up costs for customers and reduces choice on our shelves.
“It is progress that all sides now accept the need for change.
“A year ago, Brussels said ‘no renegotiation’ and Sinn Fein and the Alliance Party were calling for the protocol’s ‘rigorous implementation’.
“We now need to see the words turned into action so stability can be restored to Northern Ireland.”