Ap Iorwerth had set out a range of demands to the prime minister in a letter sent at the start of October.
As well as calling for powers over policing and justice, and for more funding for rail projects, he called for an end to restrictions on access to the Wales reserve – spare funding that the Welsh government can store in one year to use in another.
It is capped at £350m, and the Welsh government can only draw down £125m and £50m for resource and capital spend respectively per year.
The Welsh government can also borrow up to £1bn for infrastructure, with a limit of £150m a year.
Ap Iorwerth said: “There were some real positives here.
“On fiscal flexibility, the ability for us to use our funding better in Wales, use our reserves better in Wales – and on borrowing powers, I was told clearly that its now was a matter of how and when. That is a significant step forward.”
He said there was “clearly an interest” for the prime minister to “really understand that sheer injustice of underfunding of rail in Wales that we have seen for many years”.
“That is a particular issue we will be taking forward now between my office and his,” he said.
On policing, the first minister said “I think instinctively the prime minister wants to go there and there’s still work to do”.
At a speech this month the first minister called for “practical agreement” on how the two governments could work together on the economy, calling for Westminster to avoid duplication in areas that are devolved already to the Welsh government.
Burnham said Friday’s meeting was “positive”, and that both first ministers had agreed to “work together jointly on regional empowerment in Scotland and Wales as well”.
“We now have a process where we have detailed work by officials on both sides to see if we can come to a set of arrangements that are right for Scotland and right for Wales,” Burnham said.
“We had a good discussion today on two fronts, one around re-industrialisation and the offer of more devolution of innovation funding to the regional level.”
He said it was for Scotland and Wales to decide how that looks.
Burnham also said the UK government will now look at arrangements for further devolution of employment support.
Welsh Secretary Stephen Kinnock fiscal flexibilities and borrowing was on the agenda for future Welsh government discussions with No 10 North.
“It is going to take some conversations on how that would work in practice.
“I can’t give you a specific time frame as things stand,” he said.
Following Wednesday’s Budget, which saw an extra £450m announced for Wales over the next three years as well as funding for individual projects, the Welsh government claimed the extra money would represent a real-terms cut to its own finances.
A £30m funding pledge for a new railway station in Cardiff was also described as “an insult” by Wales’ transport minister.
On Radio Wales Breakfast on Friday before the summit, ap Iorwerth said there were “paltry sums of money coming on rail, when they’ve said there’s £14bn on the way” and a “real terms cut in the money we have to spend on public services”.
“The Budget was not serious about Wales,” he said.
He said in another interview he could “only assume that the prime minister is holding something back”.
