Suella Braverman has called on Rishi Sunak to "own" the poor results for the Tories in England's local elections.
"The plan is not working," the former home secretary said, urging the PM to "change course" and swing to the right.
Ms Braverman, an MP and previous Tory leadership candidate, said there was not enough time to change leader before a general election, so it was up to Mr Sunak to "fix this".
But Transport Secretary Mark Harper insisted the PM's plan "is working".
The Conservatives are licking their wounds after a string of local election defeats, losing control of 10 councils and over 470 council seats.
The re-election of Ben Houchen as the Tees Valley mayor on Friday provided respite for the party, but the loss of the West Midlands mayor Andy Street on Saturday evening was a blow.
The Conservatives also lost the Blackpool South by-election – Mr Sunak's seventh by-election defeat since he took control of the party.
"There is no disguising the fact these have been terrible election results for the Conservatives," Ms Braverman told the BBC's Sunday with Laura Kuenssberg.
"I'm urging the prime minister to change course, to – with humility – reflect on what the voters are telling us and change the plan and the way that he is communicating and leading us."
Ms Braverman said although she regretted backing Mr Sunak for the leadership it would now be "impossible" to change leader with a general election due within about six months and there was "no superman or superwoman out there".
She added: "Rishi Sunak has been leading us for about 18 months, he has been making these decisions, these are the consequences of those decisions, he needs to own this and therefore he needs to fix it."
Setting out a potential course of action, Ms Braverman said the problem was Tory voters were "on strike", saying they were telling her "you're not a Conservative party any more", and Mr Sunak needed to show "he really cares".
She said: "He needs to actually lower taxes in away that people will feel, not tweaking around the edges.
"If he's serious about migration, he needs to put a cap on legal migration, he needs to take us out of the European Convention on Human Rights – that's how you actually send the message that he's serious about stopping the boats."
When challenged on evidence moving further to the right would buoy Tory prospects, Ms Braverman replied: "The evidence is that people are not voting for what he's doing… They don't feel the benefits."
She added many Conservative MPs were privately "demoralised" and "at this rate we'll be lucky to have any Conservative MPs at the next election".
Despite the poor results, there has been no move against Mr Sunak from rebels within his own ranks, with one former minister telling Laura Kuenssberg: "There just isn't the impetus to roll the dice one more time."
Labour's campaigns chief Pat McFadden hailed the "tremendous" election results for the party, especially winning the West Midlands mayoral race which was "beyond our expectations".
"These were tremendous local election results, a tremendous by-election, and a set of mayoral results," he said, adding people can see "a changed Labour Party from a few years ago, a Labour Party that is passing the essential tests of trust that the voters look for – can you be trusted with public money and can you be trusted with national security?"
But Mr McFadden acknowledged Labour's position on the Middle East had cost the party at the local elections.
He said: "There will be some people who maybe voted Labour in the past who haven't in the local elections because of this issue and where that's the case we'll work to get people's support back."
'Not a foregone conclusion'
Defending the Conservative's general election chances, Mr Harper said there was still "all to play for" in a general election and insisted the government's plan "is working".
Pointing to the Rwanda plan, he said: "The plan is about delivering – the plan is working but we haven't got all the way through to the end of it yet.
"I think people want to see delivery, so they want to see inflation continue to come down, they want to see the boats stop, they want to see NHS waiting lists continue to fall."
He added the election outcome was closer than the polls had suggested it would be, pointing to a hung parliament, so "the election isn't a foregone conclusion".
Aside from Mr Sunak's own position, the dire local election results for the Tories open up the possibility of further internal wrangling about the future direction of the party.
Following his defeat, Mr Street pointed to the close result in his mayoral battle, where he lost to Labour victor Richard Parker by just 1,508 votes.
In defeat, Mr Street suggested the fact he came so close proves the value of 'moderate' Conservatism – the opposite of Ms Braverman's prescription.
Mr Sunak will be facing calls from those like the former home secretary, who say he needs to be more radical, meaning his finds himself pulled in two directions.