IRISH foreign affairs minister Charlie Flanagan, who attended the meeting at Stormont House, said he hoped progress on legacy issues would be achieved "shortly".
He added: "It behoves both governments and the Executive here in Belfast to ensure we stretch ourselves to finding an accommodation on the issues.
"We owe it to victims, we owe it to families, we owe it to communities, and I don't underestimate the challenge but I do believe we cannot continue to stall this matter for the foreseeable future."
First Minister Arlene Foster and Deputy First Minister Martin McGuinness held talks with secretary of state James Brokenshire and Irish Minister of Foreign Affairs Charlie Flanagan at Stormont House on Wednesday.
Justice Minister Claire Sugden also took part in the quarterly review meeting to assess the implementation of the Stormont House and Fresh Start agreements.
While progress has been made in a number of areas since the 2014 and 2015 deals, a row continues to stymie the establishment of new mechanisms to deal with Northern Ireland's toxic past.
Proposed mechanisms to address the needs of victims and an accompanying multimillion-pound government funding package are stuck in the starting blocks owing to a wrangle linked to the potential non-disclosure of British state papers on national security grounds.
The package agreed by Stormont leaders and the British and Irish governments, which includes a new investigations unit, a truth recovery mechanism, an oral history archive and enhanced funding for Troubles-related inquests, will not become reality until the logjam is cleared.
The national security dispute is primarily between the British government and Sinn Féin. However, the Democratic Unionists are refusing to sign off on the funding boost for legacy inquests until all the other issues are sorted.
Ahead of the Wednesday's review, Mr Brokenshire said: "These quarterly meetings are an important mechanism to drive forward close working towards implementing the Fresh Start and Stormont House Agreements. The UK government remains committed to full and faithful implementation of both agreements, including the establishment of the new institutions to address the legacy of the past."
"Good progress has been made on implementing the agreements. This includes legislation on welfare reform, a Joint Agency Task Force to tackle cross-border organised crime, an executive strategy to disband paramilitary groups and a new Independent Reporting Commission to report on progress towards ending paramilitary activity.
"We are working closely with the executive and the Irish government on outstanding commitments. Constructive work continues between the UK government, the Northern Ireland Executive and the Irish government, with progress on the outstanding points in relation to legacy. There is still work to do, and everyone in the current process must play their part."
"Delivering these is essential for building a brighter, more secure future for Northern Ireland – where politics works, the economy is strong and society is more united, freed from the malign impact of paramilitary activity and associated criminality."
Ahead of the meeting, Mr Flanagan will host a reconciliation event in east Belfast. The Irish Department of Foreign Affairs and Trade's annual Reconciliation Networking Forum brings together organisations and individuals working on building better relations on the island of Ireland.
"I look forward to participating in the Reconciliation Networking Forum in Belfast," he said.
"Some 95 organisations will be represented and participants will have the opportunity to explore and debate some of the key issues facing civil society today, including the challenge of moving beyond the legacy of paramilitarism. This will be the 11th year we have held this forum and it is always an important opportunity to engage with and listen to those working on the ground to further reconciliation."
On the review meeting at Stormont House, Mr Flanagan described it as an "important opportunity for the two Governments and the Northern Ireland Executive to come together and work on our shared objective to achieve full implementation of the Stormont House and Fresh Start Agreements, which provide a vital framework for Northern Ireland in the period ahead."
