The first minister’s stance on Brexit is “confusing” and “not sustainable”, a senior Welsh Labour source has said.
On Wednesday, Mark Drakeford said “we’re very near” the point a further referendum should be called.
But he stressed the priority should be to allow time for MPs to reach a consensus on a Brexit deal.
The source, who did not wish to be named, told BBC Wales Mr Drakeford should be “clearer in calling for another referendum”.
The criticism of Mr Drakeford, on Friday, came as Prime Minister Theresa May tries to persuade MPs for a third time to back her Brexit deal.
The Commons will vote on her withdrawal agreement by 20 March, after MPs agreed to ask the EU to delay Brexit beyond the current 29 March departure date.
The source said Mr Drakeford’s lack of clarity at such a crucial time on the Brexit process was “causing some tension within the cabinet” of the Welsh Government.
“It’s not sustainable to carry on saying that the view of the Welsh Government hasn’t changed when so much has changed over the past two and a half years [since the referendum],” the source said.
“The position is confusing. He should be clearer in calling for another referendum.”
During last year’s Welsh Labour leadership campaign, the two candidates who challenged Mark Drakeford both supported another referendum on Brexit.
Vaughan Gething, the Health Minister and Eluned Morgan, the International Relations Minister, were strong supporters of a so-called People’s Vote.
Former First Minister Carwyn Jones has also come out in support of a further referendum.