Immigration is not “a key issue” facing Wales ahead of next year’s Senedd election, Plaid Cymru leader Rhun ap Iorwerth has said.

The issue did not relate to real problems facing voters in their day-to-day lives, ap Iorwerth suggested.

In an interview with Nick Robinson’s Political Thinking podcast, the Ynys Môn Senedd member re-iterated his view that polls suggest he could lead a minority administration after next May’s election, making him the first ever non-Labour first minister.

The Welsh Conservatives accused Plaid’s leader of being “out of touch and in denial”.

Ap Iorwerth’s comments come after Plaid Cymru won last month’s Caerphilly by-election, beating Reform UK who have called for stronger controls on immigration.

Eluned Morgan’s Labour trailed in third, the party’s first defeat in Caerphilly since the constituency was created at a Westminster level more than a century ago.

Immigration powers rest entirely at Westminster, rather than Cardiff Bay, meaning Welsh ministers can lobby the UK government on the issue but have no ability to make changes themselves.

Asked about the divide between Plaid and Reform’s approach to immigration, ap Iorwerth said: “I don’t think it’s a key issue.

“I absolutely accept that it has become an issue and people have been told that this is something that relates to their everyday lives. I don’t believe it does.

“But that doesn’t remove it from the political sphere as an issue. And clearly, the way UK governments fail to deal with migration and border control is something that needs to be addressed, of course.”

“It’s our job on the more progressive side of politics to say listen to our arguments on what the real problems are,” he added.

Asked if, as first minister, he would support an increase in migration in order to fill vacant jobs, he said: “It’s not a matter of saying we need more immigrants.

“People move across borders and it’s really important that governments have effective ways of dealing with that and deciding who should be able to move and who should be able to stay and so on.

“But absolutely, we have to recognise that whether it’s our university sector who need students to come in, or whether it is the care sector at times, while of course training up our own young people is your front and centre.

“Of course we have, and will, depend on other people coming here too, and that’s been a positive for us.”

Darren Millar, who leads the Conservatives in the Welsh Parliament, strongly disagreed with ap Iorwerth’s views on the relevance of immigration to people’s lives.

“Anyone who claims that immigration is not a key issue in Wales is out of touch and in denial,” he said.

“It’s frequently raised by constituents and money spent on benefits, housing and healthcare for illegal immigrants is money that we cannot spend on Welsh citizens.

“You cannot fix a problem unless you acknowledge it,” he added.

Ap Iorwerth also suggested in the podcast interview that Plaid Cymru “doesn’t really wrap itself in the Welsh flag much”.

“I was looking at photographs of a Labour conference recently where there was an unfurling of a massive Welsh flag on the stage by the first minister,” he said.

“It’s not something that I’ve ever felt the need to do, and I see the populist right is trying to take ownership of the flag, be it through the… hoisting of them up and hanging them by cable ties on lampposts.

“It’s not the way I do Welshness. Yes, of course I’m hugely proud of our flag, but that’s not expression of my Welshness, it’s about sort of building a society and building a future for my country.”

Asked about forming a minority government – running Wales without a majority in the new 96-member Senedd – he said whoever was first minister would “set the tone” for the government, and would have to “build relations…get support either on legislation by legislation, issue by issue, to give stability and move Wales forward in that way, but under new leadership”.

He also said he was pleased there had been no investiture ceremony to mark Prince William becoming Prince of Wales in 2022, saying it could have been “divisive”.

“I’m a republican, as a matter of principle, and always have been,” he said.

“Politically, it’s not a priority for me, but that’s where I instinctively lie, knowing that the Royal Family is very important to other people.”

You can listen to the full episode of Political Thinking on BBC Sounds. It will also be broadcast on BBC2 on Friday 14 November at 12:30 GMT and on Radio 4 on Saturday at 1730 GMT.