The prime minister has said the UK’s four nations must “move together” to devolve more power to regions and cities, following a meeting with the Scottish and Welsh first ministers in Glasgow.

Andy Burnham said he wanted to ensure no nation was “left behind” after the sit-down, which also included representatives from Northern Ireland.

SNP leader John Swinney said he welcomed recognition that “Westminster is not working for Scotland” and pledged to work “constructively and collaboratively” with Burnham, while Plaid Cymru leader Rhun ap Iowerth said the meeting was “positive”.

Both first ministers have called for a wider conversation about independence but Burnham has ruled out referendums.

Speaking after the first National Economic Council for the nations in Glasgow, Burnham highlighted plans for devolution at the regional level, saying he wanted to ensure no nation was “left behind”.

“It’s really important we all move at the same pace together, and I won’t allow anything to delay that,” the prime minister said.

“Growth can’t wait. People need to see improvements in employment and in living standards in all parts of the UK.”

Northern Ireland was represented by officials at the meeting amid the political fallout from the Drumcree parade dispute.

Ministers and representatives at the summit discussed handing regions more powers to control employment support and funding for reindustrialisation.

“It’s about creating those structures at a regional level and that is matter for Scotland and Wales to decide what that looks like in both countries,” Burnham said.

He urged the Scottish and Welsh governments to “work jointly” with the UK government on “a model of deeper devolution”.

In the context of reindustrialisation, Burnham added this could be more devolution of innovation funding.

Swinney, ap Iorwerth and Burnham also agreed during the meeting there are too many young people out of work in the nations.

The prime minister said the UK government would look at “arrangements for further devolution of employment support for young people in both Scotland and Wales”.

Devolution has been at the heart of Burnham’s policy agenda since he took his place in Downing Street this summer.

He claims “rewiring the state” and handing more control to regional mayors and authorities across England will boost economic growth.

The prime minister’s devolution at the national level has so far been less clear but Burnham has said he will listen to the administrations’ calls for further powers while advocating that they share more responsibilities with local authorities.

John Swinney said while he and Burnham disagree on independence, the meeting was “a welcome start” on further devolution.

“When the people of Scotland take issues into their own hands, the best outcomes will about,” Scotland’s first minister said.

“To that end, I will work constructively and collaboratively with the prime minister to devolve more powers from Westminster to Scotland – as long as those proposals drive economic growth that is felt in higher wages, better jobs, more opportunities for business to start and expand, and support with the cost of living.”

A Downing Street spokesperson said the UK government would review issues raised by the first minister but this would not include a second independence referendum in Scotland.

Rhun ap Iowerth said: “I was pleased to meet with the prime minister in Glasgow today where I once again pressed the need for Wales and the Welsh government to have the necessary tools to better serve our communities.

“I also reiterated the point that further devolution within Wales is a matter for the Senedd and only the Senedd.”

He added he welcomed the prime minister’s “step forward” on the Welsh government’s fiscal and borrowing powers and gave his “full support” in pushing for a stronger relationship with the EU.

The prime minister had “positive discussions” with the Welsh leader, Downing Street said.

A spokesperson added: “The first minister of Wales agreed to start a process to explore how each government could contribute to regional empowerment, reindustrialisation and achieving good growth in every postcode.”