Kemi Badenoch accused Andy Burnham of failing to do the 'difficult stuff' after he appeared on Gogglebox on Friday night.
The Tory leader said that she worried the Prime Minister was spending his time appearing on television shows rather than ensuring people were safe.
Mr Burnham became the first PM to appear on Channel 4's reality television programme in a special episode for charity Stand Up to Cancer, where he shared the stage with his close ally the mayor of Liverpool, Steve Rotheram.
The programme, which aired in full at 9.05pm, showed Mr Burnham and Mr Rotheram – as well as other famous faces such as Stanley Tucci, Paul Whitehouse, Joe Lycett and the Sugababes – watching emotional cancer stories.
One film focused on the story of Callum who was 15 years old when he was diagnosed with a brain tumour, while another film focused on the story of Shona, who was diagnosed with cervical cancer, and her husband Will, who was diagnosed with bowel cancer.
Reacting to the stories, the PM says: 'I just couldn't imagine' and 'it's devastating for that family'.
Kemi Badenoch accused Andy Burnham of failing to do the 'difficult stuff' after the Prime Minister appeared on a special episode of Channel 4's Gogglebox (Pictured with Steve Rotheram)
Ms Badenoch has cast doubt on how serious the Prime Minister was about leading the country while making light-hearted appearances on popular television shows
He said: 'The only thing that does give some hope is there is so much incredible research going on, and some of the main cancers of years ago, there's been such big progress on them.
'But it's utter devastation isn't it, if you're that couple I don't know how you cope with that.'
But Ms Badenoch cast doubt on how serious he was about leading the country while making light-hearted appearances on popular television shows.
'I worry that between the Prime Minister being on Gogglebox and then talking about stockpiling canned goods, they're not actually doing the really difficult stuff that will protect the country,' she said.
Tory MP Patrick Spencer also criticised the PM, saying he wanted him to improve the country rather than appear on television.
He tweeted: 'There's a point - as much as we appreciate our PM's efforts to appear as normal as a soggy biscuit and a pint of milk - where I (and my constituents) would like him to get on with sorting out the country's debt, deficit, energy prices, foreign conflicts, waiting lists, housing shortage etc etc etc.'
Asked about Mr Spencer's tweet on BBC 5Live, Mr Burnham insisted that he had a 10-year plan for the country.
'But I'm not going to apologise for trying to lead with a bit of levity here and there, a bit of positivity,' he added.
Mr Burnham became the first PM to appear on Channel 4's reality television programme
Mr Burnham watched emotional cancer stories as part of the Stand Up to Cancer charity which he supports
'I'm trying to give the country a lift, trying to give the country some hope.'
He added that the appearance was for the Stand Up to Cancer charity which he supports.
The PM will watch the television shows of the week in the episode and give his assessment.
Asked for his view on the Celebrity Traitors series, he said that politicians could 'spot faithfuls and traitors a mile off'.
His remarks come after he deposed Sir Keir Starmer in a bloodless coup and replaced him as prime minister.
'Well, obviously, I would say that politicians have got a lot to offer to those who are looking for tactics in relation to The Traitors,' he said.
'I think we can spot faithfuls and traitors a mile off. Our profession teaches us to do that, but it's a great programme.'
Mr Burnham is no stranger to light-hearted media appearances and has given memorable interviews about his favourite biscuits and how he makes tea.
He has previously ranked pub snacks in a video alongside Chancellor John Healey and been quizzed about his career while on a stepladder.
He has been criticised for his 'vibes-based approach' to governing and for announcing minor changes like launching a campaign against 'headphone dodgers' rather than tackling the big issues.
Asked about Ms Badenoch's comments, a Downing St spokesman said: 'The Prime Minister took part in a personal capacity in support of the Stand Up for Cancer charity, and as you know he has a long-standing commitment to supporting charities building on his work as mayor of Greater Manchester and continuing in his office as Prime Minister.'