- By Jayne McCormack
- BBC News NI Political Correspondent
They met for what the Taoiseach called a “very good meeting”.
They also met separately with political leaders, including First Minister Michelle O'Neill and Deputy First Minister Emma Little-Bengally.
Mr Sunack said the new deal would protect Northern Ireland's place in the Union.
He said the return of devolved government was a reason for hope.
Mr Varadkar would not be drawn into the question of a united Ireland, instead saying the council's attendance showed the Good Friday Agreement was working again.
He said the new ministers were “keen to get their briefs” and the Irish government was “here to help”.
Speaking ahead of the first meeting of the Northern Ireland Executive – ministers who make policy and decisions – Ms O'Neill said “today is a good day”.
Parties in his administration – his party Sinn Féin; Democratic Unionist Party (DUP); Ulster Unionist Party (UUP); and Alliance – “committed to act together”.
Ms Little-Benkelly echoed the First Minister's comments, saying they were “very conscious of the big issues that need to be tackled”.
What did Mr Sunak and NI Ministers discuss?
One of the key issues stressed by ministers is how Northern Ireland is funded.
Executive ministers have called for a new funding model that provides “long-term sustainability” for Mr Sunak, while Ms O'Neill has previously described it as a priority for the executive.
Mr Sunack described the package as a “generous and fair settlement for Northern Ireland”.
Meanwhile, Northern Ireland Secretary Chris Heaton-Harris told Good Morning Ulster that the finance committee's report found Northern Ireland was properly funded and questioned the figures ministers used to call for funding changes.
He added that civil servants “have made mistakes in the past”.
However, both the First and Deputy First Ministers said it was an issue they had raised with Mr Sunak.
Mr O'Neill said incoming ministers had “plates up to your plate” but had to have the right financial arrangements in place to deal with these.
Ms Little-Benkelly said: “We want to make sure this executive has the right tools and adequate resources.
“We're ready for that challenge, and we're ready for a very constructive work arrangement to try to tackle that problem together.”
In the letter, the new executive effectively says that unless the funding package announced before Christmas is revised, it will lead to another budget crisis at Stormont.
Ministers therefore want to resume negotiations on significant elements, particularly the “fiscal position”.
It is based on the devolved funding model in Wales, where it is recognized that demographic differences make it more expensive to provide services than in England.
The government agreed that funding for Wales should be 115% of England's level. In other words, for every £100 spent on public services in England, no less than £115 per head for Wales.
The government has adopted a similar model for Northern Ireland, with funding per head set at 124% of the UK level.
Ministers at Stormont say it is too low and has not been subject to robust independent assessment or analysis.
They believe the starting point should be 127%, a case for going higher.
The difference may seem small but over time it can mean billions of pounds of extra funding.
DUP leader Sir Geoffrey Donaldson said on Monday morning he would speak to the Prime Minister about the issue and would be “unapologetic” in those discussions.
“Northern Ireland is underfunded,” said Sir Geoffrey, who does not sit as an MP at Stormont as he is an MP at Westminster.
“The government needs to step up a bit more so our finances are in good shape.”
How did we get here?
The devolution comes after months of negotiations between the government and Northern Ireland's largest unionist party, the DUP.
Northern Ireland withdrew from devolution in February 2022 in protest at the post-Brexit trade arrangements for Northern Ireland agreed between Britain and the EU.
Last week, DUP leader Sir Geoffrey Donaldson announced that his party had reached an agreement with No 10, which would mean there would be no “routine” checks on goods crossing from Great Britain to Northern Ireland.
On this basis, he said, his party would return to government, with legislation passed at Westminster to implement more changes.
That decision culminated in a reshuffle of devolved institutions, two years after the DUP left administration.
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