Wales' new First Minister Vaughan Gethinghas said his government doesn't plan to step in to save jobs at Wales' national museums, or save the historic national museum of Wales in Cardiff.

Amgueddfa Cymru's chief executive, Jane Richardson, told BBC Wales' Sunday Supplement programme at least 90 jobs were going at the organisation and the deteriorating condition of the historic Cathays Park building could see it close.

At his first press conference since becoming First Minister, Vaughan Gething, said his government had prioritised health funding and made no promises, despite many questions, to intervene. Mr Gething chose to hold his press conference at Coleg Gwent in Ebbw Vale.

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The chief executive of Museum Wales – which has seven sites around the nation – spoke of the "extremely difficult" task of dealing with a £4.5m reduction in its budget and said charges would need to be introduced and opening times changed. Museum Wales has had a £3m reduction in its grant, but it said that because it continues to incur a year-on-year deficit of £1.5m, it had to address a total deficit of £4.5m by the end of March.

Ms Richardson did not give an exact figure for the number of jobs going at the organisation, which, according to the museum website, has more than 600 staff and about 1.8 million visitors a year but said "would be looking at at least 90 jobs and that has proven to be the case, but we're still not at a total figure yet".

She said there was a "massive" problem with the condition of National Museum Cardiff. "Unless we're able to secure more funding for that building that will have to close," she said. She said Cardiff council had already shut the next door building, City Hall, which is the same age and had "exactly the same problems as us".

"So when you have water coming through and failing electrics, there is a question hanging over the future of that building anyway." "We are really clear as an organisation that that building needs urgent critical work for us to be able to continue opening to the public," said Ms Richardson.

Mr Gething said his government had prioritised NHS funding. Asked what the Welsh Government was offering National Museum Wales to help, he responded: "This neatly highlights, when we're talking about priorities and the reality of our budget settlement after a decade of austerity, when we set out in our budget our priorities that we would prioritise health, and social care and local government, that meant there were much more difficult choices to make across the range of the government.

"If you spoke to the college leadership here, they'd tell you that they could always do with more money and there's always difficult choices for them to make, if you went to a school, university, childcare, or a business, any area that has public funding you'll find difficult choices to make. If the NHS really is our priority and we are to invest in it, you can't have that consequence-free," he said.

"We set out there would be reductions in some areas and that's painful and difficult. The museum is just one of those, there are many, many, more, I don't celebrate having to make those choices but I can't be honest with the people of Wales about having priorities if I'm not prepared to make choices."

Mr Gething said he would "much rather we had the money required to deliver excellent public services, and support growth in the economy, that's what I want to be able to do now, and in the future."

"We need to have priorities, we have to make choices," he said. Mr Gething said at the press conference, at Coleg Gwent in Blaenau Gwent. He said the Welsh Government had done "extraordinarily badly" in terms of budgets, and £1bn being taken from it "had consequences".

"I would like to see a future where the National Museum in Cardiff is able to do the work required on the building and deliver an excellent public service...that requires difficult choices about how we grow the economy across Wales," he said.

When asked about the Welsh Government recently celebrating the arrival of a Van Gogh portrait at the museum, and now saying it would not prioritise saving the building hosting the painting, Mr Gething said they were two different things. "I think there's two separate points, the first is the capital challenges we have with an old historic building, like the museum in the middle of Cardiff and how that's maintained but making sure we're still ambitious about what we're going to do with collections because I recognise the soft pound is really important, but also the whole offer for why people would want to come to Cardiff or any other parts of Wales where the national museums are located whether St Fagans, the slate museum or west Wales."

He said: "We should still have ambition for what our national museum and galleries can provide, I think Amgueddfa Cymru has been ambitious about what it wants to do and the Van Gogh loan and exchange is just one example of that".

At his press conference, Mr gething was also asked about what had happened to all the money that was donated for his leadership campaign. Previously, on March 27, Mr Gething told WalesOnline he had not yet calculated the finances of his leadership campaign and whether all the money had been spent or whether the money, as rules dictate, would go to Welsh Labour. Then, Mr Gething said it would be a "few weeks". Today we asked him again, and he said: "I can't remember the exact number of days, whether it's 30 days or 60 days that you get to finalise your accounts. I'm going to finalise the campaign accounts and if there is any money left over it will be provided to Welsh Labour as the rules of the contest require. I need to go through the final bills, the accounts, make sure they're signed off so I don't get myself into trouble with the Electoral Commission, or the Senedd, in terms of declarations and when that is ready it will be published in the normal way," he said. "That will be the same for the other campaign," he added.