Welsh Labour should use the system that brought Jeremy Corbyn to the helm of the UK party to elect its next leader, Finance Secretary Mark Drakeford has said.
In November, the party's ruling body decided to reject one-member-one-vote.
Mr Drakeford has joined three other Labour AMs in a campaign for the issue to be decided at party conference.
But Welsh Labour leader Carwyn Jones - who has backed the decision - said that cannot happen.
He said that conference had already decided to hand the issue to the Welsh Executive Committee (WEC).
Mr Drakeford was one of more than 50 party members from 19 constituencies who met to discuss the issue at Llandrindod Wells' Metropole Hotel on Saturday.
He was joined by Labour assembly backbenchers Mike Hedges, Julie Morgan and Mick Antoniw at the meeting.
The WEC agreed to retain the electoral college system for future leadership elections - where members' votes are weighed equally with those of trade unions, affiliated groups, MPs, MEPs and AMs - when it met in November last year.
Following a consultation, it rejected one-member-one-vote (OMOV) - which has been used in the two Labour leadership elections where Jeremy Corbyn was successful and where party members' votes are all considered equal.
Advocates of OMOV say the system is more democratic, but those who support the electoral college have argued that it reflects the links the party has with trade unions.
Mr Drakeford, Mr Hedges and Mrs Morgan all back OMOV.
Mr Antoniw has supported the electoral college but thinks its balance should change and how the WEC took the final decision.
The campaign is expected to try to force a vote on the issue at Welsh Labour conference, the next of which is taking place in April.
The finance secretary said: "I have always believed that the leadership of the Labour Party in Wales should be elected on the basis of OMOV.
"I also believe that a decision of this significance should be made at a conference of the party. I therefore fully support both aims of this campaign."
Pontypridd AM Mr Antoniw said there was a strong feeling at the meeting that "because these are such important constitutional issues, and constitutional reforms, that it should be the Labour party Wales conference that is the final determiner".
Darren Williams, himself a WEC member and secretary of pro-Corbyn group Welsh Labour Grassroots, said officials from 19 constituency Labour parties took part in the meeting.
"We need to ensure that there is full debate on this issue and that the final decision is made in as open and democratic a way as possible," he said.
First Minister Carwyn Jones told BBC Wales that the Welsh Labour conference had decided that the Welsh Labour executive "would take the decision as to how leadership contests were run and the basis of which they were run in the future and the Welsh Labour executive took a very clear decision as to how that should happen".
Mr Jones said there is "no way now really for that to go back to conference".
Chairman of the WEC Mike Payne said it was a "wilful misrepresentation to suggest that this decision hasn't already been considered by conference".
He said it was "deeply disappointing to see colleagues attempting to subvert the party's democratic processes with furtive meetings which exclude members from the trade union movement".
Mr Payne accused the organisers of Saturday's meeting of excluding "substantial sections of the party in an attempt to silence dissenting voices".
"I hope that colleagues will reflect on their behaviour, accept that a democratic decision has been taken and turn their attention to taking the fight to the Tories at Westminster," he said.
A Welsh Labour spokeswoman said: "The WEC itself is representative of the whole Welsh Labour family. It is made up of elected representatives of CLPs, trade unions and other affiliates, and elected politicians such as councillors, MPs, and AMs.
"All members of the WEC are democratically elected by their constituent groups."