Showing there is no such thing as a “free lunch.”

Mayor Bill de Blasio ’s administration has no plans to expand a free-lunch program to elementary and high school students, New York City’s schools chancellor said Wednesday, setting up a battle with the City Council and advocates who have been championing free lunches for all students.

Last year, Council Speaker Melissa Mark-Viverito listed universal free lunches as one of the council’s highest priorities for the current city budget, which began July 1. During negotiations with the mayor, the council agreed to a pilot program that both the mayor and the council said would involve “all” middle school students beginning last September.

In a meeting Wednesday with editors and reporters from The Wall Street Journal, Carmen Fariña, the schools chancellor, said only a portion of middle-school students were included in this year’s pilot program and that the administration would consider expanding it to all middle-school students.

Asked if the administration would support expanding free lunches to students in elementary schools and high schools, as the council has demanded, Ms. Fariña said, “Actually not at this time, but I never say never.”

This month, Mr. de Blasio released a preliminary budget proposal for the fiscal year that begins July 1 that didn’t include funding for any expansion of the free-lunch program. A spokesman for Mr. de Blasio didn’t respond to a request for comment on the chancellor’s remarks.

A spokesman for Ms. Mark-Viverito, a Manhattan Democrat and close ally of the mayor, said “The council’s goal has been to expand to all schools.”

The council intends to advocate in this year’s budget negotiations free lunches for all 1.1 million school children, the spokesman said. There are currently 170,000 middle-school students who are eligible free lunches as part of the pilot program, according to the Education Department.