Welsh Labour MPs Tonia Antoniazzi and Ruth Jones told BBC Wales they both thought Sir Keir had “done the right thing”.
One Labour minister who did not wish to be named said “many” in the UK government had wanted Sir Keir to announce his departure.
“It’s never pleasant and sad for him personally, but the most important thing is to do what is best for the country – and this is,” they said.
Former first minister Mark Drakeford said he hopes Manchester mayor Andy Burnham will become prime minister, having campaigned together in the recent Makerfield by-election which saw Burnham elected as an MP.
“I think he has an ability to persuade people in this country to have some hope again about the future,” Drakeford said.
“People have lost faith in the possibility of improvement.”
He said Burnham, who has announced he will stand to replace Sir Keir, has “seen devolution from both ends of the telescope” and had “run a major local authority and has seen devolution from that local perspective as well”.
But another Welsh Labour source added that while Burnham would need to engage with the Welsh government “in a positive and proactive way”, he “also needs to be unafraid of calling them out”.
“Right now the Welsh government has a shopping list significantly larger than its wallet,” the source said, saying he would need to help the government prioritise the cost-of-living crisis.
In a press conference, ap Iorwerth said: “If it is Andy Burnham that is in Number 10, one would hope that his understanding of devolution, through his time as the mayor of Manchester, would perhaps give him a greater understanding of what the importance of getting devolution right is.
“But whoever holds the key to 10 Downing Street, my asks will be the same.”
