According to a written statement from the Welsh government, Sir Keir said he was “keen to establish ways of working based on shared interests” with the new Plaid Cymru administration.
In return, ap Iorwerth said he wanted the develop “a constructive relationship” between the governments.
According to the statement: “The first minister made clear he will wish to negotiate on the Barnett formula, fair funding, borrowing powers, rail and further devolution.
“The first minister noted that a Senedd majority, including the Labour group, is in favour of enhanced powers.”
It added that the prime minister “confirmed that he would be open to a conversation on powers relating to devolution”.
The Welsh government said the first minister also sought cooperation on the impact of the conflict in the Middle East on the cost of living.
Ap Iorwerth also had phone calls with the leaders of the devolved governments in Scotland and Northern Ireland.
“All agreed to work constructively on issues of shared interest,” said the Welsh government statement.
Others familiar with the conversation said that the Welsh government’s briefing was broadly accurate. They said that the first minister brought up independence, adding they were surprised it had come up in the first conversation with the prime minister.
According to a Plaid source, ap Iorwerth told Sir Keir he would guide a national conversation regarding Wales’s constitutional future.
Writing on X, Plaid’s leader in the House of Commons Liz Saville Roberts said this was something ap Iorwerth had made clear throughout the election campaign.
‘That does not mean a referendum now. Labour know that,” she said.
A Downing Street spokesperson said: “The prime minister spoke earlier today with the new First Minister of Wales, Rhun ap Iorwerth, to congratulate him on his election victory and appointment.
“They discussed working together constructively in the national interest, including on easing the cost of living and our domestic response to the Middle East crisis, and agreed on the importance of partnership to deliver for the people of Wales.
“The prime minister invited the first minister to meet in person in June, alongside the first minister of Scotland and the first minister and deputy first minister of Northern Ireland, to continue discussions on shared priorities.”