Mr Luxon suggested this week parents dissatisfied with the new school lunch programme should "make a Marmite sandwich and put an apple in a bag" for their children instead.
East Otago High School principal Helen Newcombe said the prime minister’s comments were out of touch.
For most families, providing a packed lunch for children was doable, but there were others without food at home, she said.
Yesterday at a press conference in Cromwell, Mr Luxon said it was not his comments that were out of touch, rather the comments made by "a principal like that" and the Labour Party were "absolutely out of touch".
"Great parents" were making exactly the kind of lunch he had described.
There were some challenges with "some of the food not being up to scratch", but Associate Education Minister David Seymour was working his way through it.
"We have kids going to school without lunches and that’s why we have a school lunch programme."
While in Central Otago, Mr Luxon toured the Hector Egger New Zealand Cromwell factory, a joint venture between Swiss company Hector Egger and New Zealand partners that produces structures and prefabricated materials for commercial and residential construction.
The factory was a good example of combined overseas and domestic investment, he said.
As a company it could grow faster because of capital, connection and knowledge.
He also toured Highlands Motorsport Park with Waitaki MP Miles Anderson and took part in a five-lap go-kart race with Mr Anderson, press secretary Shannon Stewart and Highlands’ resident racer Paul Blomqvist.
The prime minster finished last, but joked he managed to beat David Hasselhoff’s time.
He was also asked yesterday about Foreign Affairs Minister Winston Peters’ firing of High Commissioner of New Zealand to the United Kingdom Phil Goff after Mr Goff’s comments about United States President Donald Trump.
Mr Luxon said he fully supported the decision to sack Mr Goff because his comments had been undiplomatic.
The decision Mr Peters made was "brilliant and entirely appropriate".
He was then asked about the comments Mr Peters made about how he "made" Mr Luxon prime minister.
"I’d just say I’m very pleased I made Winston Peters the minister of foreign affairs.
"I think what the whole country’s grateful for is that we don’t have Christopher Hipkins as prime minister."
