First Minister Mark Drakeford has said there should be another referendum before Britain leaves the EU.
The move follows the European elections in which Nigel Farage's Brexit Party gained two MEPs and won 19 of the 22 council areas in Wales.
Labour finished behind Plaid Cymru for the first time in a Wales-wide vote.
Mr Drakeford cited the risk of a hard-line Brexiteer Conservative prime minister as the reason for backing a new referendum.
The first minister clarified Welsh Labour's position following fresh pressure from pro-Remain Labour MPs and AMs in the hours after the election results were announced.
"Ever since the referendum in 2016, the Welsh Government has respected the result by arguing for a form of Brexit which would protect Welsh jobs and our economy," he said.
"Labour colleagues in Westminster have done the same, most recently in negotiations with the UK government.
"The election of a new Conservative leader changes all of that. It eliminates the chances of any agreed form of Brexit, and it hugely increases the very real danger of a catastrophic no-deal exit from the EU.
"We cannot and will not stand by while that takes place.
Vote totals and share
- Brexit Party - 271,404 - 32.5%
- Plaid Cymru - 163,928 - 19.6%
- Labour - 127,833 - 15.3%
- Lib Dems - 113,885 - 13.6%
- Conservatives - 54,587 - 6.5%
- Green - 52,660 - 6.3%
- UKIP - 27,566 - 3.3%
- Change UK - 24,332 - 2.9%
"Faced with the damage of a hard-line, Tory Brexit, Welsh Labour believes that the final decision must be made by the public in a referendum.
"And, for the avoidance of any doubt, a Welsh Labour Government would campaign, in such a vote, for Wales to remain in the EU.
"We will work with any others who seek the same outcome."
Too late now. But @fmwales needs to follow this up with real actions and to show the real principled leadership that was missing in this campaign.— Alun Davies 🏴 (@AlunDaviesAM) May 27, 2019
Mr Drakeford's comments echo calls by senior Labour figures at Westminster including deputy leader Tom Watson.
However, Labour leader Jeremy Corbyn has refused to explicitly back the idea of another referendum - despite increasing calls from within his party to do so.
All 28 EU member states have been electing MEPs to the European Parliament.
The Brexit Party, launched by Nigel Farage six weeks ago, has so far won 29 out of more than 60 declared UK seats, with a total of 73 up for grabs.
Ex-Welsh Government minister Alun Davies said the move by Mr Drakeford was "too late" while Cardiff South and Penarth MP Stephen Doughty backed the first minister adding: "Crucially he is saying that it would be best off for Wales to stay in the EU."
Earlier, Plaid Cymru leader Adam Price told BBC Radio Wales' Breakfast with Claire Summers that he would look to explore the possibility of a "fully-fledged electoral pact" between Remain parties to take on the Brexit Party.
He said: "If there is a snap general election, it will almost certainly be fought, particularly on this Brexit issue, and we should get our acts together."