LODI, Italy — At the beginning of the school year, as most of the elementary students chatted over warm plates of pasta in the cafeteria, about a dozen immigrant children unwrapped sandwiches around three tables in a spare classroom with slanted purple blinds, drab office furniture and a form reading, “Students who bring lunch from home.”

“I wanted to go back to the cafeteria,” said Khadiga Gomaa, a 10-year-old Egyptian girl.

Khadiga and the others did not belong to an Italian breakfast club of poorly behaved students. They were segregated from the rest of the pupils at Lodi’s Archinti school because they had lost their daily lunch subsidy.

And that was because they failed to meet a new, and critics say punitive, requirement introduced by the town’s mayor, a member of the governing and anti-immigrant League party.