The two first ministers met Burnham separately on Thursday afternoon.
Speaking afterwards, ap Iorwerth said he was pleased to meet the new prime minister and congratulated him on his new role.
“I welcomed the opportunity to begin a new chapter in the relationship between our respective governments, based on mutual respect and a shared commitment to delivering for the people we serve,” he said.
“I know that Andy Burnham shares my belief in the power of devolution to change people’s lives for the better. In that spirit, I set out the case for Wales to have parity of powers with Scotland through a new Wales Bill with an immediate emphasis on devolving policing and justice, and a fairer funding model to replace the outdated Barnett formula.”
He also said they had discussed the cost-of-living crisis and adopting “a more collaborative approach to politics”.
“I look forward to further positive and productive discussions as I continue to make the case for fairness and equality for Wales and all its communities,” he said.