Boris Johnson has appeared unable to explain his party's claim that there would be 52 more murders a year under a Labour government.
The prime minister was pushed on the figure, used by home secretary Priti Patel, after the Tories were accused of releasing "more dodgy numbers".
The party has published analysis claming that a Labour government would lead to there being 882 more guns and 8,596 weapons on the streets every year.
This would cause up to 4,000 more violent assaults, 150 sexual assaults and 52 murders a year, the Tories claimed.
Speaking to LBC, Mr Johnson appeared to have no idea about the source of the figures.
Asked where the numbers had come from, he said: "I'm sorry I haven't been able to...you must forgive me Nick...".
He then continued: "What Priti is getting at is the reality that unless you have a tough approach on law and order, unless you back the police, unless you're able to put more police out there in a consistent way and give them the powers they need, you will find knife crime continues to be a problem, you will find serious youth crime continues to be a problem."
When LBC presenter Nick Ferrari suggested that "there is nothing to back up these figures" Mr Johnson said: "She's making a point about crime figures and the need to have robust policing, and I back that idea all the way."
Labour had earlier accused the Tories of publishing "dodgy" statistics.
Diane Abbott, the shadow home secretary, said: "These are more dodgy numbers from a Tory party that cut the police and presided over a rise in serious and violent crime.
"Labour has consistently argued that we need more police and investment in all the areas of neglect that have contributed to rising crime. The Tories are trying to distance themselves from their own record in government. You cannot have safety and security on the cheap."
The figures published by the Conservatives appeared to be based on the number of crimes prevented by police using stop and search powers. While Ms Abbott and Jeremy Corbyn have previously voiced concerns over the use stop and search, there is no suggestion that Labour would abolish the power completely.
In a foreword to the Tory document, Ms Patel wrote: "Diane Abbott has said stop and search is ‘unhelpful’. She wouldn’t back the police to use tasers to apprehend the most violent criminals.
"Jeremy Corbyn voted against mandatory sentencing for second time knife possession and thinks those ‘found in possession of a knife and convicted of that have not necessarily committed a crime’. For the first time, this analysis sets out how tragic the consequences of this could be during any given year under a potential Labour government."
During his interview with LBC, Mr Johnson also fuelled confusion over his position on Heathrow expansion by suggesting that he would try to fulfil a promise to "lie down in front of the bulldozers", despite parliament having approved a third runway at the airport.
Asked about the promise, made when he was Mayor of London, he said: "I don't see any sign of any bulldozers yet...I would have to find some way of honouring that promise. It might be technically difficult to achieve, but yes.. Let's wait and see when the bulldozers arrive.
"The issue with Heathrow is that there is still substantial doubt about the ability of the promoters to meet their obligations on air quality and noise pollution, but as you know parliament has voted very substantially in favour of that project, so that's where we are on Heathrow."
The prime minister also hinted that he could scrap HS2, having already commissioned a review of the project, and claimed that the cost of the new high-speed train line was likely to rise above £100bn.
He said: "For a new administration coming in with a project north of £100bn, it's only responsible to the taxpayer to ask whether it's being sensibly spent and whether that funding is being prioritised right - could you spend it more sensibly in the north?
When it was pointed out that the current HS2 budget is £88bn, not £100bn, Mr Johnson said: "Looking at the way things go, I think it probably will come in north of £100bn but at the moment its £88bn. That's a lot money and there will be serious questions about whether we are spending in the right order."
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