Ap Iorwerth hosted the pro-independence first ministers of Scotland and Northern Ireland in Cardiff last month and jointly declared that “Westminster’s time is coming to an end”.
In his 2,000-word letter to Burnham, ap Iorwerth made a detailed case for the transfer of powers over policing and justice, rail infrastructure, and the Crown Estate, external to Wales.
He also called for “funding arrangements that are fair, needs-based and reflect Wales’ demographic and economic realities”.
He said that “Wales’ constitutional settlement should continue to evolve to improve democratic accountability, boost growth, strengthen public services and deliver better outcomes for our communities”.
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.”
