“This is homegrown terrorism for real,” Mr. Horovitz said. He was joined at the podium in the middle of the park by several imams, a rabbi and a half-dozen elected officials, who led the crowd in singing the national anthem, “We Shall Overcome” and “This Land Is Your Land.”

Reports of hate crimes in New York City have increased over 30 percent this year, to 328. Anti-Semitic hate crimes rose to 111 from 102. Muslims were the target of 25 reported attacks this year as of Nov. 13, compared with 12 over the same period last year, according to data compiled by the police. (Mr. Yauch was born to a Jewish mother and a Catholic father and converted to Buddhism.)

Speaking at the Abyssinian Baptist Church in Harlem on Sunday, Gov. Andrew M. Cuomo, a Democrat, announced measures to fight the offenses, including the creation of a State Police unit that would combat what he called the “explosion of hate crimes in our state.” The new unit would consist of investigators who specialized in bias crimes and who would aid the state’s district attorneys in prosecuting them, according to the governor’s office.

Adam Yauch Park, a small triangular space in an upscale neighborhood, was thronged with hundreds of people, some of whom climbed the playground equipment and sat on the monkey bars. They lined State Street when the park became too full, holding children and shaggy dogs. One woman breast-fed an infant while she stood cheering. A few held signs that riffed on lyrics once sung by the artist and activist for whom the park was named. “No Sleep Till No Hate in Brooklyn,” one placard read, a reference to a Beastie Boys anthem.