Wales' first minister has called on Theresa May to respect the "majority will" of parliament and rule out a no-deal Brexit, after MPs opposed leaving the EU without an agreement.
Mark Drakeford said the UK government must take decisive action.
MPs passed a motion opposing a no-deal Brexit - but also passed a motion calling for changes to the PM's deal.
Welsh Secretary Alun Cairns said the latter vote gave Mrs May a mandate to renegotiate.
On Tuesday a majority of MPs backed an amendment - proposed by Sir Graham Brady and backed by the prime minister - calling for "alternative arrangements" to the Irish backstop, an insurance policy in the Brexit deal to avoid a hard border with Ireland.
Labour and Plaid Cymru figures criticised the PM's strategy, with one senior AM calling it a "fantasy".
MPs also passed a non-binding amendment calling for the House of Commons to not allow the UK to leave the European Union without a deal.
It comes weeks after Parliament rejected Theresa May's withdrawal agreement with the EU in a historic defeat.
Ahead of a meeting with Theresa May on Wednesday, Mr Drakeford said: "It is staggering that the prime minister should support calls to renegotiate the backstop. Only two weeks ago she said this was impossible.
"With no new ideas and red lines firmly still in place, the UK government is simply running down the clock in a vain hope that their deal will pass. Today has lost us more crucial time and the UK government must take decisive action and act on the majority will of Parliament to rule out no deal."
Tonight was Westminster at its worst. We needed a way forward. We needed leadership. What we got was a dishonest British political class, facing both ways, whistling in the wind with its fingers in its ears as the world says, no, you can’t have your imaginary cake and eat it.— Adam Price (@Adamprice) January 29, 2019
But the Secretary of State for Wales Alun Cairns said the vote shows the PM "can negotiate deals. For the past two weeks, she's been working in the national interest."
"She will now go to Brussels with the mandate to renegotiate our exit from the European Union," he said.
President of the European Council Donald Tusk said the withdrawal deal is "not open for re-negotiation".
Welsh Brexit minister Jeremy Miles said the PM's strategy was a "dangerous mess" and "fantasy politics".
Plaid Cymru's Liz Saville-Roberts said "chasing unicorns is not a plan".
She said the prime minister was insisting on "pursuing the undeliverable". Her party leader Adam Price said Tuesday night was "Westminster at its worst".
AMs are voting on Brexit in the Senedd on Wednesday, although it is not yet clear what the terms of the debate will be.
BBC Wales' Brexit correspondent James Williams says Mr Drakeford wants to strike an agreement with Plaid Cymru on a motion for that debate.
Mr Price called on the first minister to back a further referendum on leaving the European Union.
"If the Welsh Government brings forward such a motion it will have Plaid Cymru's full support so that Wales sends out a powerful message, that it is the electorate that must now be allowed to decide the way forward," he said.
The PM’s strategy is a dangerous mess. Pressing Tory MPs to back changes to her own deal that she claimed was the only game in town last week. And the EU27 won’t remove the backstop whilst she clings on to her red lines. “Alternative arrangements” is fantasy politics.— Jeremy Miles AC/AM (@Jeremy_Miles) January 29, 2019
Welsh MPs voted on party lines on Tuesday night.
Almost all of Wales' 28 Labour MPs - with the exception of Paul Flynn who has not been attending Parliament - voted against a no-deal Brexit and against Sir Graham's amendment.
All Welsh Tory MPs voted against the no-deal Brexit motion except Guto Bebb, the pro-EU MP who represents Aberconwy.
Former Welsh Secretary Stephen Crabb did not take part in the vote on the backstop amendment, which Tory MPs had been expected by their party to support.
Mr Bebb voted against Sir Graham's backstop amendment, while the remaining Welsh Tories backed it. He said he was "very pleased" MPs have stated that they oppose a no-deal Brexit "despite huge effort from whips".
Chris Davies, the Conservative MP for Brecon and Radnorshire, said he was disappointed that the no-deal amendment passed.
"Members of the House of Commons have taken away the main negotiating card," he said.
But he said that Sir Graham Brady's amendment meant there was a "very good chance the country will end up leaving the EU with a deal".
Pro-Brexit AM Mandy Jones tweeted that the "the passing of the Brady amendment gives the PM a strong hand".