Nigel Farage's Brexit Party gained two Welsh MEPs after a sweeping victory in the European elections in Wales, winning in 19 of the 22 council areas.
Plaid Cymru kept its MEP, coming second, with third-placed Labour taking the fourth seat, ahead of the Lib Dems.
The Tories lost their seat and dropped to fifth in the vote, just ahead of the Green Party, UKIP and Change UK.
Welsh Labour leader and First Minister Mark Drakeford said the party would now back a Remain vote in a new referendum.
Brexit Party MEP Nathan Gill said the election result was a "very strong message from Wales - we want our Brexit and we want it now".
It means Mr Gill, first elected in 2014 under the UKIP banner, retains his seat in Brussels as a Brexit Party MEP, alongside his new party colleague James Wells.
Mr Gill said only his party was "committed to respecting the vote of the people of Wales" to leave the EU in the 2016 referendum.
All 28 EU member states have been electing MEPs to the European Parliament.
The Brexit Party, launched by Nigel Farage six weeks ago, has won 28 out of the 64 declared UK seats, with a total of 73 up for grabs.
"It's going to be a pain in the backside for the EU I should imagine," Mr Gill said.
"We're not going there to make it work, are we? I mean, we told them, let Britain leave the EU with a decent trade deal and you won't have any problems with Nigel Farage ever coming back.
"They didn't do that, did they?"
Jill Evans stays as Plaid Cymru's MEP and Jackie Jones replaces Derek Vaughan and retains Labour's Welsh seat in the European Parliament.
It is the first time Plaid has beaten the Labour Party in a Wales-wide election, and only the second time Labour has lost such a poll in a century.
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%
Plaid leader Adam Price said the result was "incredible" and it "shows that the tectonic plates of Welsh politics are shifting".
"Support for the Westminster establishment parties is crumbling and Plaid Cymru is preparing to form the next government of Wales in 2021," he added.
Ms Evans said: "Plaid's manifesto set out a vision for a thriving future for Wales at the heart of Europe. I'm looking forward to throwing all my energy into delivering it."
The turnout was 37.1%, up 5.6% on the previous EU election in 2014.
Mark Drakeford congratulated Jackie Jones on retaining the party's seat.
He warned that the election of a new Conservative leader would increase the chances of a "catastrophic no-deal exit from the EU".
"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," he said.
Ex-Welsh Government minister Alun Davies blamed the huge drop Labour in Labour support on both Mr Drakeford and the party's UK leader, Jeremy Corbyn.
"This is the reality we face. Poor leadership from London and no leadership from Wales," he said on Twitter.
Tweeting ahead of the results, former Welsh Labour First Minister Carwyn Jones said a key message of the night was the failure of pro-EU forces to present a united front.
"Remain parties will comfortably out-poll the Brexit Party in Wales tonight, but the Brexit Party will come first in the vote tallies," he said.
"This is why I said we should have put forward a united slate, just like the Brexit Party."
These results are extremely disappointing for our hard-working candidates and the Party must now reflect long and hard on them. Here in Wales, @WelshConserv will continue our hard work in the Assembly holding this failing Welsh Labour Govt to account.— Paul Davies AM/AC (@PaulDaviesPembs) May 26, 2019
Mr Price agreed, telling BBC Radio Wales' Breakfast with Claire Summers: "I would like to explore the possibility of a fully-fledged electoral pact between Remain parties.
"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."
Welsh Liberal Democrat leader Jane Dodds seized on her party's fourth place as evidence that its "fightback is in full effect".
"Voters are listening to us again, supporting us again and believing in us again," she said.
"These results show we're on course to return a strong and effective Welsh Liberal Democrat assembly group in 2021."
Cadan ap Tomos, chairman of the Welsh Liberal Democrats National Executive Committee, told BBC Radio Wales that he was feeling "absolutely fantastic" about the result.
Reacting to coming in fifth place - down from third in the previous European election in 2014 - Conservative Welsh Assembly group leader Paul Davies called the results "extremely disappointing for our hard-working candidates".
The results in Wales show that in @WelshLabour we have some questions to ask ourselves. Pro referendum & remain parties gained more votes than leave parties. The room for a middle of the road approach has disappeared & attempting more of the same will not serve us or Wales well.— Vaughan Gething AM (@vaughangething) May 27, 2019
The party "must now reflect long and hard on them", he added.
Lead Tory candidate Dan Boucher emphasised the "very challenging circumstances" of the poll, which took place because the prime minister had failed to secure the UK's departure from the EU on 29 March, as she had promised.
"People were very frustrated that Brexit hasn't been delivered and I'm personally frustrated that Brexit hasn't been delivered as someone who campaigned for it," he said.
"It's a very strong signal to the government."
Brexiteer David Davies, MP for Monmouth, said the results were "an unmitigated disaster for the Conservative Party".
He added that ministers should stop "whinging" about Brexiteers like Boris Johnson and "take some responsibility for the shambles they have helped create by failing to deliver Brexit".
The Green Party took 6.3% of the Welsh vote and its leader in Wales, Anthony Slaughter, said the election was not just about Brexit.
"Public concern for climate change has never been greater," he said. "The people demand action, and the Green Party is the only party that promises to do that based on a record of real delivery."
Analysis, BBC Wales political editor Felicity Evans
This is an extraordinarily bad night for Welsh Labour, a party that has topped every Wales wide poll (except one) for a century.
It may be the victim of a UK-wide issue and the ambivalence of Jeremy Corbyn's position on another EU referendum.
But the Welsh party has defied the UK trend many times before. And for their new leader, Mark Drakeford, presiding over a result like this is damaging.
Sources say the party in Wales had no control over the conduct of the campaign or party policy on Brexit.
What we do know is that Mr Drakeford has, for months, resisted pressure from within his own Welsh party to come out more strongly for a further EU poll.
It was loyal to the UK party position, but was it the right call?