The First Minister has called on MPs to put their "country first and find a compromise" after parliament voted to reject Theresa May's Brexit deal for the third time.
Mark Drakeford, unlike many in his party who are now calling for a second referendum, said MPs should first try to come to an agreement on the next stage of Brexit negotiations.
He tweeted, "if this fails, then the only way forward is to take the decision back to the people through a public vote".
After a heated debate in the Commons, Theresa May's deal lost by a majority of 58 - with 344 voting against the motion, compared to 286 voting in its favour.
It means the default position now is for the UK to leave on April 12, with or without a deal.
Speaking after the results of the vote were announced, the Prime Minister said the implications of the vote were "grave".
Meanwhile, Welsh Secretary Alun Cairns argued the Brexit deadlock is the fault of the Labour party.
"A general election is the last thing the country wants. I don't think the public will look kindly on what the Labour party have done."