The scheme provided meals to 287,000 children in its first year, at a cost of £135m. It is currently in its second year, with the cost having risen to £140m.
The policy is currently being budgeted for on a year-by-year basis.
The mayor said: "We will be publishing our budget in due course and setting out confirmation that this policy will carry on next year."
He added: "My promise to Londoners is for as long as I am mayor, children going to state primary schools will receive this offer of a universal free school meal."
Khan was re-elected in May and his third term of office ends in May 2028.
Speaking to the London Assembly’s budget committee, Richard Watts, the mayor's deputy chief of staff, said “the scheme has been enormously successful” and “all the benefits that we hoped we would see based on previous evidence we are now seeing city wide”.
However, he said next year’s funding for the scheme was not in place yet.
He said: "The whole of the mayor’s budget is £130m, we think free school meals will cost £140m next year so even if we canned everything else that we did, universal free school meals will never be met from the GLA (Greater London Authority) mayor budget.
"Therefore we will announce that funding in the group budget papers in due course.”
Khan launched the scheme in 2023 as a one-year emergency measure to help families with the cost of living, paid for using higher than expected business rate receipts.
In January this year, he announced that he had extended it for a further 12 months, to cover the 2024-25 academic year. It was again funded largely using business rate receipts which were “more buoyant than we expected”.