Mayor Thomas M. Menino said yesterday that he is expanding his ban on sugar-sweetened drinks in schools to include all city properties and functions, a sweeping restriction that means that calorie-laden soft drinks, juices with added sugar, and sports drinks like Gatorade will no longer be offered in vending machines, concession stands, and city-run meetings, programs and events.

“It’s going to be bad for morale around here,’’ said Jim Hardy, who runs Station 10 Cafe at police headquarters, where officers get daily doses of soda, fruit juices, and sugary iced tea, along with their sandwiches.

The mayor, who has battled weight issues, said that too many Bostonians are overweight or obese and that he wants to make healthy choices easy for them.

“I haven’t had a glass of soda in two years,’’ Menino said during a press conference at City Hall announcing the measure.

The move follows other anti-obesity initiatives across the country, including the fight against childhood obesity by Michelle Obama at the White House, as communities grapple with a problem deemed a national epidemic.

Yesterday, Carney Hospital in Dorchester followed Menino’s lead, saying it will ban sweetened beverages on hospital grounds. Hospital president Bill Walczak called on other health institutions to follow Carney’s plan.

“We all know that good health is built around a couple of things,’’ such as exercising and eating healthy, Walczak said. “So why do we spend so much effort in providing unhealthy food in our cafeterias, vending machines, and various other institutions? It just doesn’t make sense.’’

Barbara Ferrer, executive director of the Boston Public Health Commission, said the new city policy will curb health care costs and boost worker productivity. She said 1-in-3 Boston public high school students and 1-in-2 middle and elementary school students are overweight or obese.

While soda and sweetened beverages are major contributors, Ferrer also faults a super-sized culture and the abundance of inexpensive processed food in supermarkets.

In efforts to promote healthier eating, Boston has pushed for farmers markets selling fresh fruits and vegetables, backyard gardens, and neighborhood walking groups.

In 2004, the city fought off huge resistance and banned junk food and soft drinks from vending machines at Boston public schools. This summer, the city is planning to launch a bike share program that would make 600 bicycles available for borrowing.

“We’ve made tremendous strides in changing the food and beverage environment in the city, and creating more opportunities for residents to be more active,’’ said Ferrer.

The mayor’s executive order sets so-called science-based, color-coded standards for what is considered a healthy beverage and what can be sold or served on city property.

City buildings and departments have six months before they are required to phase out the sale of beverages coded red: those loaded with sugar, such as nondiet sodas, presweetened iced teas, refrigerated coffee drinks, energy and sports drinks, and juices with added sugar. The promotion of red beverages on banners, panels, and vending machines will be banned.

The new policy allows for the sale of yellow beverages such as diet sodas, diet iced teas, 100 percent juices, low-calorie sports drinks, low-sugar sweetened beverages, sweetened soymilk, and flavored sweetened milk.

Green beverages, such as bottled water, flavored and unflavored seltzer water, low-fat milk, and unsweetened soymilk will also be allowed.

So far, the ban is getting a cool reaction from some independent contractors who serve city employees. John Moreira, who manages the Coffee Stop Cafe on the first floor of City Hall, spent a part of the afternoon turning around bottles to scan the nutrition labels, trying to guess which drinks would no longer be allowed. He said that he will conform to the new policy, but that he has reservations.

At police headquarters, Hardy said the new plan could curb 20 percent of his business if officers and civilian employees begin bringing in their own sodas and eventually sandwiches, instead of buying them from him.

Yesterday, he said, complaints were coming in from those who love their sodas and do not like being told what to do or to drink.

“The city banned saturated fat two years ago, and they can do without,’’ Hardy said of the officers. “But I don’t think they can do without their’’ Coca-Colas.

Meghan Irons can be reached at mirons@globe.com.

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