Labour leadership hopefuls want 'more autonomous' Wales
Labour leadership candidates Andy Burnham and Liz Kendall have said the party's Welsh and UK branches must work together.
Mr Burnham told BBC Radio Wales he had asked the first minister to lead a "constitutional convention" looking at the relationship between the UK Labour party and Welsh Labour.
But he rejected the idea of a more federal structure.
Ms Kendall pledged to introduce much closer working if she wins.
She was speaking in the Senedd after holding talks with the first minister.
Ms Kendall said focusing on Wales was as much a priority for her as the south of England, and Scotland, where the party suffered heavier losses.
She said: "We have a huge amount to learn from what Carwyn Jones and other Welsh assembly members are doing here.
"I think we need a much closer working between the Welsh government and Labour in future."
Mr Burnham said it would be wrong for the party to have different "messages" in different parts of the country.
Earlier this month, the Welsh government Public Services Minister Leighton Andrews renewed his calls for Labour to move to a federal structure that would give more autonomy to the Welsh and Scottish Labour parties.
He tweeted: "I really don't care who English Labour choose #federallabournow."
Mr Burnham said: "I think it would be a mistake to start saying 'oh we speak to this group of votes over here with this message and a different message over here'.
"In Wales, I think I saw similar factors that were in play in England [at the general election].
"People [were] going to UKIP because perhaps they had doubts about our record on immigration and leaving Labour for that reason."
On the UK party's relationship with Welsh Labour, Mr Burnham said the Labour party needed to get the right relationship between the two.
"That's why I've asked Carwyn Jones to lead a UK constitutional convention to really look at these questions in detail," he said.
"What is the right balance across the UK between the UK role and then a stronger Welsh role?
"I want to see a more autonomous Wales within a stronger UK.
"I want... Labour not always looking grudging on devolution and being dragged to positions.
"I think we now need to get on the front foot and I hope Carwyn's going to help us do that."
Ms Kendall added that she wanted to be a leader "working in strong partnership with Carwyn and Labour people around the country", and that the way Wales is funded needed to be looked at.
She said: "As we change the constitution and devolve more power and control, we need a fair funding formula in Wales, Scotland and England too.
"That is essential if we are to make sure the Welsh assembly has the power and the responsibility to improve people's lives."