The Irish and British prime ministers said on Wednesday that they were open to considering reforming Northern Ireland's Good Friday peace accord, but that any debate could only happen when the powersharing government underpinning it was restored.
Irish nationalists and pro-British unionist politicians are obliged to share power under the deal, but the ability of the largest party on either side to pull down powersharing for long periods has been identified by many as a block on progress.
That, coupled with the rise of the Alliance party, which identifies as neither nationalist or unionist, has sparked calls for an overhaul of a political architecture that the largest unionist party, the DUP, has boycotted for more than a year.
"I think it's the shared view of the British and Irish government that there is a conversation that needs to happen about reforming the Good Friday Agreement. No agreement should be set in stone forever," Varadkar told reporters after an event to mark 25 years of the peace accord.
"I think there is a time and a place to have that debate but it should happen when the assembly, the executive, north/south ministerial bodies are up and running because people will be in a different mode then."
Sunak said in a speech that he understood the frustrations of those seeking changes but that any conversation about reform could only begin once the powersharing executive was up and running and must be backed by all communities.
Both he and Varadkar encouraged the DUP to end its protest over post-Brexit trade rules. Sunak said he would listen to the DUP's concerns and continue to try to persuade them to accept recent changes to the trade rules.
"I urge you to work with us to get Stormont (Northern Ireland's assembly) up and running again," Sunak told unionist politicians.
(Writing by Padraic Halpin; Editing by Alex Richardson)