Jonathan Pryor, Leeds City Council's executive member for learning skills and employment, said photos circulating today on social media were "beyond belief".
Images shared online showed poor quality and low value packages sent to families during the lockdown.
Downing Street has said the contents of some free school meal food parcels sent to families are “completely unacceptable” and that the Government is urgently looking into the issue.
The council uses an in-house service, Catering Leeds, instead of some of the private firms that have been criticised.
Leeds East MP Richard Burgon has also written to Education Secretary Gavin Williamson about some of the "shamefully inadequate" offerings.
Coun Pryor said: “What we have seen this week with regard to free school meals has been absolutely appalling.
"It is a complete disgrace that some of our most vulnerable children are being left to go hungry as some private companies seek to place profit above the needs of children.
"The pictures that have been posted on social media show families receiving boxes including half a tomato, half a pepper and a third of a carrot.
"It is beyond belief that anyone can think this is an acceptable way to treat children who are then expected to fully engage with home learning."
Schools are able to choose whether to go with private providers or the council.
Leeds City Council currently provides free school meals for 187 primaries, two high schools and a further education institution.
Roundhay Primary headteacher Alastair Field said Catering Leeds "have done an exceptional job since March."
He added: "We cannot praise them enough.
"The team have worked incredibly hard and do everything with such a moral purpose in their hearts."
Cllr Pryor added: “The Government needs to introduce stricter monitoring of just what is being provided and penalties for companies who are found to be taking advantage of the hamper scheme.
"As a local authority we are stepping in where we can and delivered over 7000 hampers ourselves last week, something we will continue to do.
“It is absolutely vital that children receive adequate and nutritious food and to see the pictures of what some companies are providing is shocking, this can’t be allowed to continue and the Government needs to intervene now.”
In his letter, Mr Burgon said photos shared online were "clearly not an isolated incident"
He added: "Parents have made clear that the boxes that have been provided to them are totally inadequate to feed their children, and would not provide a remotely balanced diet.
"The Royal College of Paediatrics and Child Health called the boxes 'an insult to the dignity of people who rely on this support; they are absolutely right."
Chartwells, the education food service company, said it is fully investigating the images of food parcels circulating on social media, but the company believes many of them are not its hampers.
A spokesperson for Chartwells said: “We take our responsibility to provide children with access to nutritious food very seriously.
“We have worked hard to produce food hampers at incredibly short notice during these challenging times.
“Our hampers follow the DfE specifications and contain a variety of ingredients to support families in providing meals throughout the week. In the majority of instances, we have received positive feedback.”
The Prime Minister’s official spokesman told a Westminster briefing: “We’re aware of those images circulating on social media, and it is clear that the contents of those food parcels are completely unacceptable.
“The Department for Education is looking into this urgently and the minister for children, Vicky Ford, is speaking to the company responsible and they will be making it clear that boxes like this should not be given to families.”
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