Vandalism to monuments memorializing America’s military heroes, like the theft in Staten Island earlier this year of plaques honoring chaplains who gave up their life vests as the World War II ship Dorchester was torpedoed, is a particularly obnoxious act of civic destruction that warrants a new anti-vandalism law, several City Council members said yesterday.

“This is so frustrating to me that we have to deal with these low-life, misfit creatures who deface these public monuments,” Council Member Michael Nelson, a Democat of Brooklyn, said.

Mr. Nelson is among several lawmakers who back legislation introduced by Council Member Michael McMahon, a Democrat of Staten Island, to target people who desecrate military memorials.

“There are vandals who are out there and don’t respect and don’t understand the sacrifice and the commitment to our country that was shown by generations of veterans,” Mr. McMahon said.

The Parks Department said it supports Mr. McMahon’s bill but urged the council to broaden its efforts to include all types of monuments.

An assistant parks commissioner, Jack Linn, recalled pranksters who once tossed a Peter Pan statue from Carl Schurz Park on the Upper East Side into the East River.

Vandals who are caught are currently charged under graffiti and criminal mischief statutes. The bill’s supporters want the special law to discourage vandalism against memorials to America’s military heroes.

After the hearing, Mr. McMahon said he would likely re-introduce two separate bills to target all monument desecration, but one would reflect particular disgust for vandalism of military monuments.

Mr. McMahon’s bill, which committee aides say is modeled on a Missouri statute, would create a new misdemeanor to punish vandals of military tribute monuments with up to a year in jail and a $2,500 fine.

Parks Department officials say they have difficulty quantifying how often monuments are targeted. They estimate that the department spends more than 15% of its $400,000 monument-maintenance resources on undoing vandalism.

But the cost to the community can be more profound than dollars and cents, Mr. Linn said. He spoke of damage done to the Triumph of the Human Spirit statuary in Foley Square. Yesterday evening, a group of teenage skateboarders were using the granite abstract monument depicting slave ships as a skating ramp.

“You go there and you’re ashamed,” Mr. Linn said, “You’re ashamed of a society that does this to its public art, to its public monuments. You’re ashamed to be a member of it.”