First Minister Rhun ap Iorwerth has demanded a “new deal” for Wales from the UK government that would put the country on an equal footing with Scotland.

In a letter he requested powers over policing, justice, rail and the Crown Estate top be transferred to Cardiff.

In a speech at Plaid Cymru’s conference in Llandudno, the party’s leader said Prime Minister Andy Burnham has promised him he would not undermine Wales.

The UK government said it was “committed to building a stronger and fairer Wales in a stronger and fairer United Kingdom”.

Plaid Cymru is gathering in Llandudno’s Venue Cymru for the first time since it won a historic victory at the Senedd election in May.

Plaid had won power for the first time, ending Labour’s 27 year control of the Welsh government.

The first minister said the result amounted to a “new dawn” for Wales.

But he warned that the upcoming Welsh government budget process would be “tough”, and said he would have to “find savings where we can”.

Speaking to party activists, ap Iorwerth said: “I do believe the new prime minister and I both want to have a constructive and positive relationship.

“I’ve looked him in the eyes and said do not undermine Wales as a nation. Do not bypass our Senedd. And he looked me in the eyes and promised he would not. I will hold him to that.

“Wales will hold him to that.”

Scotland’s government and parliament has more control over the country’s own affairs than Wales, where policing and justice are controlled in Westminster, and not Cardiff, and where rail is largely devolved.

Ap Iorwerth said his proposed “new deal” would “redress the historic unfairness of our fiscal and constitutional settlement and put Wales on an equal footing with Scotland as a bare minimum”.

“It remains my hope that the prime minister will listen in a shared spirit, and that he’ll see that the respect agenda between the Welsh and UK governments must work both ways,” he said.

“If he fails, Wales will know again that our best interests will never be served by Westminster, and that it matters little whether who lives in Number 10 Downing Street is an Evertonian or an Old Etonian.”

Ap Iorwerth has sent a 2,000 word letter to Burnham spelling out his requests.

He said his meeting with Burnham at the Commonwealth Games “did leave me feeling positive – here we had an experienced devolutionist who wanted to bring power and people closer together.

“But as the weeks went on, it became increasingly clear that the prime minister’s wave of new powers risked crashing against Offa’s Dyke.”

He accused Burnham of having a “devolution programme for England”.

Plaid Cymru won the largest number of seats at May’s election, and since the defection of Sarah Cooper-Lessad it has 44 in the Welsh Parliament chamber.

It is five short of a majority, and needs the help of at least one other party group to pass its spending plans next year. It has been in talks with Labour, the Tories and Reform.

Ap Iorwerth acknowledged a “difficult economic and fiscal backdrop” and said it would be a “tight budget”.

“There will be difficult decisions. The budget arithmetic requires us to be disciplined and resourceful.”

He acknowledged the need for a “serious and collaborative approach with other parties”.

“We’ll have to drive efficiency, improve productivity and find savings where we can; through consolidating and streamlining services, avoiding duplication and focusing on outcomes.”

But he said that had to be “free of the damaging approach of the parties on the right”, accusing them of defining “savings” and waste by “ideology”.

He said the UK government’s forthcoming autumn budget was a chance to “reverse the planned-real terms cuts” to the Welsh government’s own spending.

Plaid has long-called for Wales to receive substantial extra funds for rail. Ap Iorwerth said that should come “now, not the 2030s”.

The party leader paid tribute to fire services who fought the summer’s wildfires, and said he would “not allow my government to burden my children and your children with the destructive legacy of complacency on climate change”.

Criticised during the election campaign for the amount of plans or reviews Plaid Cymru promised to commission, ap Iorwerth said he would “never apologise for putting the time in to fix the foundations because this government refuses to be a house built on sand.”

He said they had provided an “immediate cash injection to prioritise the longest NHS waits”, and had moved “quickly to begin the rollout of the most generous childcare offer anywhere in the UK”.

The party eventually plans to roll out childcare to children as young as nine months before the next election.

The first minister said his government was “determined” to tackle the NHS, saying “too many aspects of the service are unfair on patients and on our brilliant staff” and are “unsustainable for the future”, although he acknowledged he could not change the NHS “overnight”.

He said he would not “shy away” from tackling child poverty “because of a difficult economic and fiscal backdrop”.

Ap Iorwerth is expected to meet the prime minister, along with the first ministers of Scotland and Northern Ireland, at the end of the month.

Burnham had previously said he would be “open” to the idea of giving the Welsh government control over policing.

He has also said: “I have to respect the governments in the nations of the UK, and I will, and give a fair hearing to anything that is put to me.”

A UK government spokesperson said: “This government is committed to building a stronger and fairer Wales in a stronger and fairer United Kingdom.

“That’s why our focus is now on working with the Welsh government to empower local leaders and communities to deliver good growth and jobs in every postcode.”