For some low-income Long Island children, a free or reduced-price school lunch might be the only nutritious meal they eat all day.

A federal program that begins Tuesday in locations across the Island extends those free lunches through much of the summer. Some sites started offering the meals last week.

“If they have the need in the school year, they’ll have the same need in the summer,” said Lillian Pennon, who helps run the program at Galilee Church of God in Christ in Riverhead.

Some low-income parents cannot afford nutritious food, Pennon said. Others work in the day, and their kids may eat junk food rather than the fresh fruit, sandwiches and carrots served through the summer food program, she said.

The U.S. Department of Agriculture funds the effort, which began in 1968. About 3.8 million people up to age 18 received food last summer, but that’s a fraction of the 22.1 million students who participate in the school lunch program, a USDA spokesman said. Breakfast is served at some sites.

Long Island Cares and Island Harvest and are among the groups that distribute food to churches, libraries and nonprofit groups located in neighborhoods with a large number of low-income families.

The program eliminates a major expense for parents, said Serena Tyson, director of the program at Bethel Christian Church in Massapequa.

“It alleviates the pressure for families who are struggling to make ends meet,” she said.

Nutritious food provides “a healthy mindset for kids,” she said. “They’re able to read and able to learn.”

About 110 kids are signed up for the program at Boys & Girls Club of the Bellport area. The last day of classes for local schools was June 24, and the organization started its summer food program three days later.

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“This might be the only meal they get for the day,” said Demetria Guirantes, program supervisor.