Tánaiste and Minister for Foreign Affairs Micheál Martin said the people of Northern Ireland deserve government.
He was speaking after meeting the five main Stormont parties in Belfast amid the impasse within the power-sharing institutions.
"In a democracy, when people elect their public representatives they expect them to take their seats both in the Assembly and in government," he said.
"The context is there in terms of the negotiations and discussions that are under way between the United Kingdom Government and the European Union team.
"I made the point to the parties this morning there is a significant degree of confidentiality surrounding those negotiations and discussions, and I am in agreement with the need to provide space to both the negotiating teams to see if they can bring about a resolution of the issues around trade.
"There are a lot of challenges, I would not understate the difficulties that both sides will face in trying to resolve the issues, but I think the sensible thing to do is allow the EU and the UK to continue with the negotiations.
"Meanwhile the parties here will have to focus on the imperative of getting the Executive and the Assembly restored."
Mr Martin also said the EU is sensitive to concerns unionists have about the Northern Ireland Protocol. He said the discussions were useful to pick up on issues.
"I think Europe is very aware and sensitive of the points of view and concerns that the unionist community have put forward in respect of the protocol issue, and having that seamless trade within the UK single market," he said.
"These are issues that have been advanced strongly by the unionist parties, both the DUP and the UUP, and other parties are clear that if issues of that nature can be resolved, they're happy enough to see them resolved.
"I do genuinely believe that the European Union is very anxious to deal with those concerns that unionism has."
DUP leader Jeffrey Donaldson said he has restated his position to Mr Martin that his party will not re-enter devolved government at Stormont until the protocol is replaced.
Speaking after his meeting with Mr Martin, Mr Donaldson said it had been a "useful and constructive conversation".
"Over 18 months ago we outlined the parameters for the way forward. We set our tests and those continue to be our yardstick for measuring any deal between the EU and UK," he said.
"There will be no restoration of the NI Executive until the protocol is replaced with arrangements that unionists, as well as nationalists, can support. Northern Ireland's place in the UK internal market must be restored and our constitutional arrangements must be respected.
"We are seeking the restoration of democratic decision making to the Assembly, replacing the democratic deficit created by the protocol.
"Why should anyone want to deny the people of Northern Ireland, through their democratically-elected representatives, a say or a vote on vast swathes of the laws governing our economy and which affect the people of Northern Ireland so directly?"
Sinn Féin's Michelle O'Neill has asked that the EU and UK "close out" on a deal on the protocol as quickly as possible.
Speaking after her meeting with the Tánaiste, she said: "I am very much encouraged by what we're hearing, I think the Tánaiste shares that same assessment and we want both sides to continue in earnest to get a deal, to close this out, to close it out as quickly as possible."
Ms O'Neill said she was "encouraged" by what Mr Martin had said of the EU-UK negotiations.
"I think he shares the same assessment, that there does appear to be good soundings coming from what is happening.
"People seem to have went quiet, I hope that that means that they're working really hard, that they're going to get to a point where there is a deal on the protocol. I hope that that happens speedily, I would encourage both sides to continue doing what they're doing.
"Then we need to get back into the Executive, because one year on is not good enough that we're not sitting around the Executive table, and one year on is not good enough that the DUP have continued to punish the public."
Alliance MLA Paula Bradshaw said her party emphasised an urgent need to reform the Stormont institutions after the latest period of collapse.
"He said that he is in support of reform but I don't think that he has the same timescale as we would in that we should allow the negotiations with the EU to complete, get the institutions back up and then talk about how we reform the institutions," she said.
Ulster Unionist Party leader Doug Beattie has warned that unionists must not be "bounced on a deal" on the Northern Ireland Protocol.
He said he had a "very frank and very open" meeting with Mr Martin.
"We talked about the protocol, it is becoming incredibly frustrating, we are not being kept in the loop as to what is happening in regards to the negotiations between the EU and the UK, and if we're not involved, if they try to bounce unionism, it's simply not going to work," he said.
What is the NI Protocol?
The protocol is part of the Withdrawal Agreement - the international treaty under which the UK left the EU.
It was a compromise to prevent a hard border with checks on goods crossing from Northern Ireland into the Republic of Ireland and the EU's Single Market.
Under the deal, Northern Ireland left the EU along with the rest of the UK.
But the British government accepted that it would stay aligned with the EU's Single Market rules for goods.
That allowed the checks to be done at Northern Ireland's ports instead of along the 300-mile land border. It has been dubbed 'The Border in the Irish Sea'.
The EU's rules on customs and regulation of agri-food products also continue to apply to goods arriving in NI.
Mr Donaldson said he also told Mr Martin that the Irish Government must "step up to the mark" over the Omagh bombing.
Northern Ireland Secretary Chris Heaton-Harris announced yesterday there would be an independent inquiry into the dissident republican blast which hit the Co Tyrone town on August 15 1998.
Mr Donaldson welcomed the move and said he urged Mr Martin that the Irish Government should hold a similar process in parallel.
"I welcome this inquiry and I pay tribute to the Omagh families who have travelled a long and difficult road," the DUP leader said.
"If this inquiry is to establish the full picture, however, that requires the Republic of Ireland to also hold a similar process in parallel.
"The bomb was placed by republican terrorists in Omagh but it was planned, prepared and transported to Omagh from the Republic of Ireland.
"I trust the Irish Government will step up to the mark on this legacy issue as well as others."
Responding to calls for his Government to step up on the Omagh bombing, Mr Martin welcomed the decision to have a public inquiry into whether the attack could have been prevented, and said ministers will "fully co-operate" with it.
"We will have to establish ourselves the precise mechanisms by which we will pursue this, either by the establishment of an inquiry in the republic or provide full co-operation in terms of documentation and so forth to the UK inquiry," he said.
"These are issues that we will examine ... but we're working on that already, we want to see the terms of reference, of course.
"On the wider point, I had pointed out to the Secretary of State this is somewhat inconsistent with the legacy bill that is currently going through Westminster, which we oppose and strongly communicated our views in relation to that legacy bill.
"In our view, as we saw recently in terms of the court decisions in respect of the killing of Aidan McAnespie, that right up to now, cases can be brought to closure, verdicts can still be issued."
Additional reporting Vincent Kearney
