Rishi Sunak and Leo Varadkar make flying visits to Northern Ireland

They met for what the taoiseach called "a very good meeting".

They also met political leaders separately, including First Minister Michelle O'Neill and Deputy First Minister Emma Little-Pengelly.

Mr Sunak said the new deal would protect Northern Ireland's place in the union.

He said the return of the Assembly was a cause for optimism.

"We've worked very hard and succeeded in protecting Northern Ireland's place in the union and built on what we achieved with the Windsor Framework to ensure the smooth flow of trade in the UK and all the benefits that are there as a result of Brexit can be seized," he said.

Mr Varadkar would not be drawn on the question of a united Ireland, instead saying that the Assembly's return showed the Good Friday Agreement was working again.

He said the new ministers were "keen to get into their briefs" and the Irish government was "here to help".

The executive has called for talks with the government on long-term funding stability to deliver public services, with Ms O'Neill saying NI's funding model was the executive's priority.

On Sunday, Mr Sunak described the package as "a generous and fair settlement for Northern Ireland".

However, in the letter to the prime minister, the executive said the additional funding "will only serve to provide a short-term solution to the pressing issues we now face".

Ms O'Neill said how Northern Ireland is funded needs to change, adding she would be "strongly pressing that point" with Mr Sunak.

Deputy First Minister Emma Little-Pengelly, who jointly leads the executive with the first minister despite their different titles, added that they will be seeking to ensure the government "provides sufficient funding in a package to fulfil its promises on public sector pay".

The letter calls for a new funding model that offers "long-term sustainability", adding that will only happen "through joint working and delivery from both your government and the executive".

Sir Jeffrey Donaldson, the DUP leader who does not sit as an MLA because he holds an MP seat at Westminster, said on Monday morning that he would be speaking to the prime minister about Northern Ireland's public finances.

He said he would be "unapologetic" in those discussions.

"Northern Ireland is funded below the level of need," Sir Jeffrey said.

"We need the government to go a bit further so our finances are in a sound position."

However, speaking on BBC Breakfast, Secretary of State for Northern Ireland Chris Heaton-Harris said the funding package was "fair and generous".

"The Northern Ireland Fiscal Council said in a report in May last year that it was funded correctly and this £3.3bn comes on top of that," he said.

In this letter, the new Executive is effectively saying the financial package announced before Christmas is almost guaranteed to lead to another budget crisis at Stormont unless it is revised.

Ministers therefore want the reopening of negotiations on significant elements, most notably the "fiscal floor".

It is based on the devolved funding model in Wales, where it was recognised that demographic differences make it more expensive to deliver services compared to England.

The government agreed that Wales should be funded at a 115% of England's level. In other words for every £100 per head spent on public services in England, there should be no less than £115 per head for Wales.

The government has also accepted a similar model for Northern Ireland with per head funding to be set at 124% of England's level.

Stormont's ministers say this is too low and has not been subject to robust independent assessment or analysis.

They believe the starting point should be 127%, with a case for it to go higher.

The difference may sounds small but over time it would represent billions of pounds of additional funding.

On BBC Radio Ulster, Mr Heaton Harris questioned whether civil servants might be wrong about the figure of 127%, adding: "They have been wrong in the past."

The secretary of state continued: "Anything that we do when it comes to public sector funding has to be based on facts and numbers rather than theory, so I am sure there will be lots of conversations based on this, but I would like to think they would be based on factual figures.

"There is a big chunk of money for public sector pay but that relies on negotiations conducted by local ministers, there's a big chunk of money that's new and we would like to see that spent on transformation of public services, and there's a big chunk of money that comes from money that previously been promised by the UK govt and not spent goes into that transformation pot."

The return of power-sharing came after months of negotiations involving the government and the DUP, Northern Ireland's largest unionist party.

It withdrew from power-sharing in February 2022 in protest at post-Brexit trade arrangements for Northern Ireland, agreed between the UK and EU.

Last week, DUP leader Sir Jeffrey Donaldson announced his party had a reached a deal with Number 10 that means no "routine" checks on goods crossing from Great Britain to Northern Ireland.

He said on this basis, and with legislation passed at Westminster to implement more changes, his party would return to government.

That decision culminated in the restoration of the power-sharing institutions on Saturday, two years to the day since the DUP walked out of the executive.