The ruckus has prompted the local mayor to suspend the measure for a month on Tuesday.
Under the announced policy, students whose parents failed to pay would be fed the so-called Tuscan fettunta - a piece of toasted bread with olive oil - instead of a full meal.
The new policy comes from Mayor Silvia Chiassai Martini, who leads the local centre-right municipal government.
The mayor said the measure had to be enforced after fees totalling 85,000 euros were not paid between September and February.
The announcement prompted protest by local public schools.
Several schools announced that they refuse to implement the policy, saying meals during school hours are part of the right to an education.
On Tuesday, however, Martini said she would give families another month to pay and their children would be granted a full meal in the meantime.
The mayor said students from families in financial difficulty will be helped by social services.
The rest will have an additional 30 days to pay before their children are fed bread and oil for lunch until the end of the school year in June.
Members of the Tuscan chapter of the centre-left Democratic Party (PD) expressed satisfaction, saying the concession was “reasonable” and “only made after the PD denounced [the measure] at all levels”.
ANSA