As part of the city government’s crackdown on fat, the schools chancellor, Joel Klein, announced a new fitness test for students yesterday – and the food industry raised alarms about the specter of a legislative assault on fast food.

With more than one in four city elementary students considered obese, Mr. Klein is expanding a new program to test students’ strength and speed and link the information to their academic achievement.

“Clearly,we have a problem with very high calorie intake and too little physical activity,” the city’s health commissioner, Thomas Frieden, said yesterday at P.S. 1 in Chinatown. Under the new initiative, parents will receive information about their children’s fitness levels along with report cards. Only schools that have physical fitness instructors will be part of the program next year.

At the same time, a council member, Joel Rivera of the Bronx, wants to fight fat by regulating where fast food restaurants can advertise and sell their fare. The proposal, which Mr. Rivera announced earlier this week, would limit fast food restaurants from opening near schools and neighborhoods with a large number of overweight children.

In New York City, Hispanic elementary students are twice as likely as white students to be obese.

While the city already legislates where people can smoke or open an adult bookshop, some legal experts say regulating where people can buy a Big Mac and fries might be going too far.

“It’s disturbingly paternalistic in saying to the public that it cannot be trusted to make its own decisions about where to shop and where to eat,” a first amendment lawyer, Floyd Abrams, said. “The right direction is education and the wrong direction is coerced deprivation of our citizens.”

“After fast food, what will come next?” Mr. Abrams, who has represented the tobacco company R.J. Reynolds, asked. During litigation over tobacco marketing, many lawyers asked the same question about what would come after cigarettes, Mr. Abrams said.

Zoning laws have been used in the past to tackle alcohol-related health problems. Obesity – which is linked to diabetes, asthma, heart disease, and cancer – is the city’s only health problem that is getting statistically worse.

A few areas across the country, like the Westwood Village area of Los Angeles near the University of California at Los Angeles campus, already place limits on the number of fast food establishments allowed.

A vice president at the National Restaurant Association, Tom Foulkes, which represents 60,000 companies, called Mr. Rivera’s fast food idea “short sighted.”

“Using the city zoning laws to address an issue as complex as obesity is misguided,” Mr. Foulkes said. He said that rising obesity rates had more to do with Americans’ sedentary lifestyle than their penchant for “quick service” food – the industry term for fast food.

Other food industry experts raised questions about how to define fast food, especially in a city where many people often get their food from local delis and bodegas.

Several years ago, an assemblyman of Brooklyn, Felix Ortiz, caused a stir when he suggested a “fat tax” on junk food to curb the obesity problem.

“We’ve been oversaturated,” Mr. Ortiz, who supports the fast food proposal, said yesterday. “I think the time has come where something needs to be done.”

Mr. Rivera mentioned the fast food idea on Tuesday but has not yet introduced a bill into the council.

In addition to banning sugary sodas from city’s schools, Mr. Klein said yesterday that the city has made great strides in introducing healthy foods. Still, about 100 middle schools don’t have physical education teachers.

The new fitness assessments, known as the FitnessGram reports, were tested in a pilot program this year that included 235,000 students. The test includes running, sit-ups, push-ups, and stretches.

Reports were sent home yesterday that indicate if a student is in the “healthy fitness zone,” and include tips for improving fitness such as limiting television and video games, drinking water instead of soda, and exercising at least one hour a day.

The principal of P.S. 1 on Henry Street, where students demonstrated the fitness test said that many youngsters couldn’t walk up to the fifth floor without getting winded.

The city’s Department of Education will be able to analyze the fitness data and link it to student performance, although it has not yet crunched the numbers for this year’s students.

Mr. Frieden declined to comment on Mr. Rivera’s fast food legislation until it is introduced.

“If we can do things that make the default decision for people a healthier choice, that’s important,” he said. “Whether it works, whether it’s legal, that has to be looked at very carefully.”