First Minister Rhun ap Iorwerth has written to the prime minister to request "a new deal for Wales" before his first Plaid Cymru conference speech since taking office.
In his letter to Andy Burnham, sent on Thursday and seen by BBC Wales, the Plaid leader called for more powers to be transferred to Cardiff.
Burnham previously said he would "give a fair hearing" to anything put to him by the Welsh first minister.
Ap Iorwerth will address party members in Llandudno on Friday, five months on from Plaid's historic success at May's Senedd election.
The result saw the party win power for the first time, ending Labour's 27 years in government since devolution began in 1999.
However, without a majority of seats in Cardiff Bay, ap Iorwerth leads a minority administration which has to work with opposition Members of the Senedd to pass new laws and budgets.
The government lost a key vote on its spending plans in July.
In his speech, ap Iorwerth will say the election "delivered a clear mandate from the people of Wales for positive change that makes a tangible difference to their lives".
"This mandate includes extending devolution to enable the Senedd and the Welsh government to have the necessary tools - powers, funding and financial flexibilities - to drive the maximum improvement in outcomes for the people of Wales by integrating and improving public services and growing the economy.
"As an underpinning principle to support these reforms, Wales should be able to benefit from the same constitutional and fiscal tools already available in Scotland."
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".
Speaking to BBC Radio Wales Breakfast, ap Iorwerth said he was looking for "practical answers to unlock those things that we need to take Wales forward".
He said he recognised there could be "practical barriers" to how the Crown Estate was devolved, and said he was "happy to look at how we do it in a gradual way, in order to make sure that it's not just an ideological drive".
He separately suggested that he may spend extra funds that come to the Welsh government, as a consequence of more funding for social care in England, on social care in Wales.
Labour's Burnham has promised to end triple lock for pensions from 2030 to fund a new national care service.
Social care is the responsibility of the Welsh government, and how it spends its money is up to its ministers. Both Plaid and Burnham would face elections before the policy came in.
Ap Iorwerth said: "When Boris Johnson was describing his plans that would have led to a consequential [from social care], we in Plaid Cymru were able to put a plan in place at that time that would allow us to spend the consequential on social care in Wales.
"I would be taking the same approach again."
Ap Iorwerth said it was a "good direction of travel" from the prime minister, but he added: "We don't know what the consequentials will be."
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."
