Ireland must hold a "similar process in parallel" to the Omagh bomb inquiry, Micheál Martin has been urged.
Northern Ireland Secretary Chris Heaton-Harris announced on Thursday that there would be an independent inquiry into the dissident republican blast which hit the Co Tyrone town on August 15, 1998.
The bomb killed 29 people, including a woman pregnant with twins, and injured hundreds of others.
In 2021, a Belfast High Court judge recommended that the UK Government carry out an investigation into alleged security failings in the lead up to the attack, and that a similar probe should be established by the Irish Government.
On Thursday, Justice Minister Simon Harris said they would await the details of the UK's inquiry before announcing what action they would take.
Foreign Affairs Minister and Tánaiste Mr Martin met the major Stormont parties in Belfast on Friday.
During his first meeting of the day, with DUP leader Sir Jeffrey Donaldson, the Tánaiste was told his government must "step up to the mark".
After the meeting, Mr Donaldson 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."
The issue was also raised with Mr Martin by the Ulster Unionist Party and the SDLP.
Ulster Unionist leader Doug Beattie said: "We did say to Micheál Martin that we believe the Irish Government needs to do more, not just on the Omagh bomb inquiry, we think they need to have their own inquiry in Ireland, but on legacy as as a whole, remembering, of course, that hundreds, if not thousands, of our citizens here in Northern Ireland were killed or injured by attacks, which came from Ireland, and the perpetrators returned back to Ireland again.
"We did make the point strongly that they need to do more."
SDLP leader Colum Eastwood said he believes it is "very clear that the Irish Government are committed to not being left behind in terms of this investigation".
"I think yesterday was a very good day for the Omagh families, it took far too long," he said.
"But I have no doubt that the Irish Government will step forward and not be left behind when it comes to investigating the Omagh bombing."
During his visit, Mr 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 powersharing 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.
"I reiterated our very strong view that the constitutional position of Northern Ireland is not impacted, and has to be underpinned in terms of the principle of consent, and that is something we strongly assert, that there can be no undermining of the constitutional status of Northern Ireland as per the Good Friday Agreement and the principle of consent.
"We believe the issues can be resolved but that is a matter in the first instance for the EU negotiating team and the United Kingdom.
"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."
However, Ulster Unionist Party leader Doug Beattie has warned that unionists must not be "bounced on a deal" on the Northern Ireland Protocol.
He was speaking after what he described as a "very frank and very open" meeting with Mr Martin in Belfast.
"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,
"We need to know what is going on and therefore we can add value by raising red flags where we see there are problems and giving solutions, and the Ulster Unionist Party have always been about giving solutions.
"But we cannot be bounced on a deal which is simply not going to work in the long term.
"It was a frank meeting. I am still frustrated that we haven't moved forward more than we have and I sense as well that Micheal Martin is also frustrated that we probably haven't moved forward.
"So, we're going to recycle these meetings again and again, and again. What we really need is a deal between the EU and the UK that everybody can buy into, unionists, nationalists, or other."