The Taoiseach said history showed that political stability in the region depended on the Irish and British governments working “in lock-step”.
Mr Varadkar made the comments on the eve of the 25th anniversary of the Good Friday Agreement, a diplomatic feat that brought peace to Northern Ireland after 30 years of bloodshed.
The 1998 peace deal, brokered by the US, paved the way for powersharing between nationalists and unionists.
Certainly over the next few weeks, I’ll be intensifying my contacts with Prime Minster Sunak and the British Government in particular, because what we know from history is that Northern Ireland only really works when the two governments work hand in hand
Despite the peace accord serving as a blueprint for other conflicts globally, there has been a powersharing stalemate at Stormont for almost as long as it as been functioning.
The latest hiatus is over the DUP’s opposition to the implementation of the post-Brexit trading arrangement known as the Northern Ireland Protocol.
In a push to revive the executive and assembly, a new agreement was struck between the EU and UK that sought to amend the protocol and resolve the concerns raised by businesses and unionists.
Although the British parliament and EU have formally signed off on the Windsor Framework, the DUP and former prime ministers Boris Johnson and Liz Truss have voted against a key element and the Democratic Unionists are yet to commit to returning to Stormont.
Speaking on Sunday, Mr Varadkar said part of the reason the framework was struck was to encourage the DUP to return to the powersharing institutions.
“We’ve put a huge amount of effort in the last few months into getting an agreement on revisions and reforms to the protocol,” he told RTE’s This Week programme.
“And that culminated in the Windsor Framework, which was agreed only in the past few weeks. That took a lot of engagement with the different political parties in Northern Ireland, with the British Government, with the European Commission.
“And one of the reasons why we did that, aside from making sure we avoid a return to a hard border, was that the agreement could potentially reopen the possibility of the DUP coming back into the executive.
“So we’ve done that piece now, and the next piece now is deep engagement with the British Government and also with the five parties in Northern Ireland to try and get the institutions up and running again.
“Certainly over the next few weeks, I’ll be intensifying my contacts with Prime Minster Sunak and the British Government in particular, because what we know from history is that Northern Ireland only really works when the two governments work hand in hand.
“One thing I’ve been struck by watching all the documentaries around the history of the Good Friday Agreement was the extent to which the Taoiseach and the Prime Minister had to be in lock-step, and now that we have the agreement on the protocol, I think it’s possible to do that.”
He added: “Certainly since Brexit, and even before Brexit, that sort of level of cooperation between the two governments, the two governments working hand-in-hand, hasn’t been the same. And that’s largely because we found ourselves in very different positions.”
When asked whether the Irish government would take an inter-state case against the British government over its controversial legacy bill, as requested by Amnesty International, Mr Varadkar said it had not been ruled out.
He said: “But taking a case against your nearest neighbour at a time when you’re trying to work with them, and work in lock-step with them as I mentioned earlier, is not without its consequences and this is a bill that has not yet passed through the Commons and Lords.
“So there’s still time for the British government to reconsider, to pause it, to make amendments to it, to engage with the five parties in Northern Ireland and the victims’ groups.”
On Tuesday, Mr Sunak will travel to Northern Ireland as part of US president Joe Biden’s much-anticipated visit to the island of Ireland for the Good Friday Agreement milestone.