Mark Drakeford has said his government could campaign to stay in the EU if the matter was put again to the public in a new referendum.
But the new Welsh First Minister’s support for a fresh poll remains conditional on Theresa May’s deal failing to pass MPs, and no election happening.
That is despite party colleagues calling for him to campaign for a poll.
An open letter said it is the only way to move past the Brexit impasse.
Meanwhile more than half of Wales’s 40 MPs have signed a letter calling on the Prime Minister to rule out a “No Deal” Brexit.
In total, more than 200 MPs have signed the cross-party letter. They include 21 Welsh labour MPs and four from Plaid Cymru.
MPs were due to vote in December on a deal negotiated by the UK government with the European Union, but ministers pulled the vote in the face of substantial parliamentary opposition to the deal.
Government sources told the BBC on Monday the vote will now take place on 15 January.
In his first press conference as first minister, Mr Drakeford said: “I’m happy for the sake of the argument to assume for a moment that on such a ballot paper there would be a choice of remaining in the European Union
“The advice of the Welsh Government in the first referendum was that Wales’ future was best secured through continued membership of the European Union. I don’t think we would have changed our minds about that advice.
“So if we were in a position of saying to people in Wales what we as a government thought the right answer would be if staying in the European Union was on the ballot paper in a referendum, I would anticipate, and anticipate pretty strongly that our advice would not have changed.”
Mr Drakeford said he was “not opposed” to a second referendum.
But, sticking to Labour party policy, he said: “There has to be a sequence of events.
“It is still not too late for Mrs May to do a deal that could command the support of the House of Commons,” he said.
“If there is no agreement in the House of commons and no general election, then I don’t see any alternative but to go back to the public and ask them to decide.”
Reiterating the Welsh Government position that a no deal Brexit would be catastrophic for the economy and should be avoided, he said in the event of that Theresa May failing to get a deal through the House of Commons “I think we will clear the assembly programme of government business on the following Tuesday”.
He said he will speak to ministers about the possibility of a website to be produced at the same called Preparing Wales “focusing on no deal preparations”.
He said Brexit would be an agenda item on all cabinet meetings from now on and “that we would have concerted activity on all fronts”.
The open letter to Mr Drakeford, from the anti-Brexit Wales for Europe group, said: “The gravity of our situation requires brave leadership and clarity from the Opposition as much as Government, as well as time to consult the public again.
“This is the only way out of the Parliamentary impasse.”
The letter said: “You have already called for an extension of the Article 50 period beyond 29 March 2019.
“But we now urge you to use your new office to its utmost to demand – of both the UK Government and the UK leadership of your own party – a new People’s Vote in which continued membership of the European Union would be an option on the ballot.
“This new public vote is necessary regardless of whether or not a General Election is called.”
Nine Labour MPs and four backbench Labour AMs – including former minister Alun Davies – signed the letter, together with 13 Plaid Cymru MPs and AMs.
It was also signed by Plaid Cymru MEP Jill Evans, Labour MEP Derek Vaughan, Welsh Liberal Democrat leader Jane Dodds and Welsh Green party leader Anthony Slaughter, three Labour council leaders and two Plaid Cymru council leaders.
Mr Drakeford succeeded Carwyn Jones as first minister in December after winning a three-way contest for the Welsh Labour leadership.
First Minister Mark Drakeford is being urged to campaign for a further EU referendum in a fresh call by members of his Labour assembly group and MPs. An open letter, also signed by leading Plaid Cymru figures and Welsh Liberal Democrats, said a public vote was the only way out of the parliamentary impasse on Brexit.