The leader of Plaid Cymru, Rhun ap Iorwerth, has vowed to form a stable minority government in the Senedd and said he would seek out mature cooperation from all opposition parties.

Ap Iorwerth said his administration would press the UK government for extra powers over policy areas such as policing and justice and focus on results rather than engaging in political rows with Westminster.

Asked if Plaid’s win meant the country had taken a step closer to independence – a key Plaid aspiration – ap Iorwerth replied that a “more confident” Wales felt closer.

“The people of Wales didn’t begrudgingly decide to give us a go,” he said. “They said: ‘We believe in your belief in Wales.’ If there’s one thing we absolutely have to bring out of this, it is a more confident nation. And I believe we’re on the way to that.”

Plaid fell short of winning a majority in the Welsh parliament, taking 43 of the 96 seats but comfortably held off the challenge of Reform UK (34 seats) and soundly beat Labour (nine), which had dominated politics in Wales for a century.

On Sunday the Green party leader in Wales, Anthony Slaughter, said his party would back ap Iorwerth’s bid to become first minister, and the sole Liberal Democrat, Jane Dodds, said she would abstain from the vote. If, as expected, the Labour members also abstain, the path will be clear for ap Iorwerth to become first minister.

The Plaid leader said he hoped a vote could take place as early as Tuesday, adding: “We are eager to press ahead as soon as we can. We want to get going.”

He said he did not see the need to work with other parties as a negative. “We have to look for positives in this. I’m sure we can build stability by putting a programme together in a way that we can attract the support of others to get things done. We’re not talking about coalitions, we’re talking about a cooperative approach.”

Ap Iorwerth said priorities included improving the health service, raising standards in education, creating jobs and rolling out a generous childcare offer.

“We will ask other politicians to ask themselves, well, why wouldn’t they want to allow that programme to go through? But with cooperation on how exactly it happens, what detailed changes might need to be introduced. Let’s do that in a constructive way.

“I expect to be held very firmly to account by the other parties. But I am making that sincere invitation to them to engage in that kind of mature politics that I think the people of Wales want and expect.”

Ap Iorwerth suggested a supplementary budget may be introduced and hinted that his cabinet could include new members as well as experienced hands.

He said he wanted his relationship with Keir Starmer – or his successor – to be constructive. “I won’t be looking for a spat. I’ll be looking for results. I will be relentless whilst constructive in doing so.” He will ask for more powers over justice and policing, devolution of the crown estate and fairer funding.

“Labour have a choice. They can decide now to somehow punish Wales for their defeat in this election or they will have to reflect on how their indifference towards Wales has now been received by the people of Wales.

“And I will be their guide towards making decisions that actually do the right thing. I have aspirations for being able to mould our own future, but currently if we’re told that this union works, well let them show it.”

Ap Iorwerth has said there could be more cooperation with the other nationalist parties in Scotland and Northern Ireland, for example on policies they have in common, including offshore natural resources. He said Wales, Scotland and Northern Ireland could stand together to fight for more equality across the UK.

Reform and Labour suggested they would be prepared to cooperate with Plaid on some issues.

Ken Skates, the interim leader of Welsh Labour after the former first minister Eluned Morgan resigned, said its relationship with Plaid would be “mature” but it would serve the people of Wales, not ap Iorwerth’s party. He also said he would love to become the permanent Welsh Labour leader.

Llŷr Powell, a prominent Reform member in Wales, said his party would not be tribal and may be prepared to vote with Plaid on policies it believed in.

Ap Iorwerth said the size of Plaid’s win reflected the determination of the Welsh people to keep Reform out as well as their disillusionment with UK and Welsh Labour.

“It also reflects that growing and palpable belief in Plaid Cymru being the party to deliver this new beginning for Wales,” he said.