Rising rates of youth unemployment have created a split at the top of government over how fast it should meet its promise to give young people the full minimum wage.

Peter Kyle, the business secretary, is understood to believe now is not the time to give 18- to 20-year-olds the full minimum wage, which Labour promised to do in its manifesto.

Others believe there is little evidence to show that recent pay rises for low-paid workers have had any effect on unemployment.

Torsten Bell, a Treasury minister, told the BBC on Friday morning: “If you look at what the Low Pay Commission said in their annual report, they didn’t find evidence that previous increases in the minimum wage for young people had had an effect on their employment.”

The splits have emerged following a landmark government-backed report this week by the former Labour minister Alan Milburn, who found that youth unemployment was costing Britain more than £125bn a year.

Milburn’s report revealed the number of young people not working or studying had surpassed a million for the first time in more than a decade, prompting calls to reduce the pace of youth minimum wage increases.

Milburn himself told the News Agents podcast this week: “To get the jobs there for them, you’ve got to make sure the employers are willing to take the risk. If you’re in, say, the hospitality sector or the retail sector, margins tend to be very low. These tend to be sectors that were really badly hit by the cost of living, hospitality in particular.”

It comes during a broader tussle over the future of the Labour party. Andy Burnham has promised a shift to the left on certain policies if he wins the Makerfield byelection and then becomes prime minister, while others have urged the party not to move from what they regard as the political centre.

Tony Blair, the former prime minister, warned in an essay this week that policies such as increasing the minimum wage – which he brought in – had created “headwinds, not tailwinds, for businesses”.

Labour promised in its manifesto to equalise the rates of the minimum wage for 18- to 20-year-olds with those of workers who are 21 and over but did not say how quickly this would be achieved. Bell said on Friday: “We’re committed to our manifesto that we stood on and we will deliver it. But that manifesto did not set out the timeline.”

While he and others in the government believe they should slow down the pace of rises in youth rates of the national minimum wage if there is evidence that it has an impact on employment, they do not yet believe that evidence exists.

The government accepted a recommendation this year from the Low Pay Commission (LPC) to increase the main rate of the minimum wage by 4.1%, but raise the youth rate by 8.5%. They now stand at £12.71 and £10.85, respectively.

The commission will tell the government in October what it is recommending for the financial year starting on 1 April 2027; some in government privately hope it will give a recommendation significantly lower than this year’s.

Earlier this year ministers even changed their guidance to the LPC to reflect the concerns in government over unemployment among young people. Where it used to tell the commission to take rates of youth unemployment into account, it has now told it to prioritise employment rates instead.

The LPC said last month it did not believe wage rises were contributing to higher youth unemployment rates. “While the commission recognises that labour market outcomes for young people have deteriorated over the past two years, we are not aware of any robust evidence that higher youth rates have contributed to these falls,” it said.

Ministers are not bound to accept the commission’s recommendations, though in practice the chancellor, Rachel Reeves, has made a virtue of doing so in the past. If they want to further slow the rise in pay for young people, they could instead change the guidance once more for subsequent years.

While ministers row over the causes of youth unemployment, MPs and trade unions are urging them not to row back on their promises to voters.

“There is no good evidence that the minimum wage has caused a jump in youth unemployment,” said Kate Bell, assistant general secretary of the Trades Union Congress. “This is a talking point which business always resorts to, but the evidence shows the picture is much more complex than that.”

Justin Madders, a former employment minister, said: “The minimum wage is set following submissions made by stakeholders to the LPC, which includes employers. That is why the rates set have always been at a level that do not impact on employment levels – a fact borne out by 25 years of evidence.”

Joanne Thomas, general secretary of Usdaw, the shop workers’ union, said: “We are deeply concerned by voices within the government suggesting that Labour’s manifesto commitment to end minimum wage rip-off youth rates should not be delivered in full.

“We are clear that the general election manifesto is for the lifetime of this parliament, and that is when the policy should be delivered.”