The prime minister has been heckled at Welsh Conservative conference after her party suffered huge losses in English council elections.
"Why don't you resign", party member Stuart Davies told Theresa May before he was shouted down and escorted from the premises in Llangollen.
Mrs May said the election results gave both the Conservatives and Labour a simple message "to get on" with Brexit.
She insisted to BBC Wales that the Welsh Conservative party supports her.
Mr Davies yelled across the hall: "We don't want you" as Mrs May began her speech to conference.
The heckler - a member of the Clwyd South Conservative association which recently passed a motion of no confidence in the PM - accused her of dragging the party into disrepute.
"We saw the results. There's only one way - it's down," he told BBC Wales after being ejected.
"We need a new prime minister and we need that new prime minister as soon as possible."
Asked if the heckler was saying what many Welsh Conservatives were saying in private, Mrs May told BBC Wales: "I think you saw the reaction from everybody in the hall. They did not want that to be said."
The Tories lost scores of seats at the ballot box in the local elections in England on Thursday. Labour also suffered losses while the Liberal Democrats, the Greens and independents made gains.
In her speech Mrs May admitted that the elections had been "difficult" for the party and that councillors had lost their seats through "no fault of their own".
She also warned of the risks of leaving the European Union without a deal, saying the party had "a responsibility to deliver something truly historic".
"What is momentous and historic is seldom simple and straightforward," the PM said.
"But I think there was a simple message from yesterday's elections to both us and the Labour Party - just get on and deliver Brexit."
Theresa May's proposed withdrawal agreement with the remaining 27 European Union states has been repeatedly rejected by MPs.
Number 10 is currently negotiating with Labour to see if the two sides can reach an agreement on the deal.
Analysis by Felicity Evans, BBC Wales political editor
Did the heckler at the beginning of the PM's speech voice publicly what Welsh Tories are saying privately?
No, says Mrs May - she told me the reaction to his intervention in the hall (he was shouted down) should tell us all we need to know about her levels of support within the Welsh party.
But while there is anger that the heckler breached Welsh party etiquette, there is a lot of talk here about the PM's departure.
"A [party leadership] contest over the summer would be best", one activist told me.
There was certainly nothing in Mrs May's speech that gave a clue about when she might depart. But she emphasised the need to deliver Brexit - as has every speech I've heard from the stage.
However, she also warned in strong terms about the dangers of leaving with no deal and once again explained the benefits of her deal - which has now been defeated three times in Parliament.
Audience reaction was subdued, but delegates know the script. Leaders get ovations at party conferences and they obliged.
Mrs May, who had previously said "no deal is better than a bad deal", used her speech to warn of the risks of leaving the European Union without an agreement.
"We need a Brexit that works for our manufactures and our exporters, that keeps supply chains flowing and opens up new routes for trade, and our deal does that," she said.
"Leaving with no deal would not."
Mrs May told the conference that departing the European Union without an agreement could risk the unity of the UK.
"Majorities in two nations of our United Kingdom voted to leave, majorities in the other two voted to remain," she said.
"In Northern Ireland there's the added challenge of a land border with the EU.
"So we need a Brexit that works for the whole of the United Kingdom, and our deal does."
Meanwhile, the party's assembly leader Paul Davies told delegates a Welsh Conservative Government "would introduce no new taxes" and "would lower taxes where possible".
Mr Davies accused First Minister Mark Drakeford of dithering over the M4 relief road, and vowed to reintroduce the right to buy social housing which the Labour Welsh Government has scrapped.
He said there was "more that unites" than divides the Welsh Conservatives.
"Changes of government and transfers of powers is a cornerstone of a democratic nation," Mr Davies told the conference.
"Thirty years of Labour rule is not healthy for our democracy and is not healthy for Wales."
"In 2021 we have a duty to offer progressive, innovative and radical alternatives, to this tired, and failing, Welsh Labour Government - and we need to make sure that we do this together."
'A lot of work to do'
Mr Davies, who was elected by Welsh party members last year, admitted in an interview that he has to raise his profile among the electorate.
"I fully accept that I have a lot of work to do," he told BBC Wales.
Opening the morning conference session, Welsh Secretary Alun Cairns also referred to his party's Brexit woes, receiving a round of applause when he said that "leaving the European Union was never going to be an easy process, but we will leave".
Mr Cairns blamed rival parties for the deadlock in Parliament, rather the Conservative MPs who had voted against Mrs May's EU Withdrawal Agreement.
"As a minority administration, we are determined to find a solution to end our opponents from blocking departure, and enabling us to honour the outcome of that referendum," he said.