A statement issued Sunday night by a lawyer, Michael Sussman, in the name of the family said Mr. Thomas “had a long history of mental illness and hospitalizations” and “no known history of anti-Semitism.”

The violence further traumatized the Jewish community in the New York region, coming after a string of anti-Semitic incidents in recent weeks. It occurred weeks after an anti-Semitic mass shooting at a kosher supermarket in Jersey City, N.J., left three people dead, including two Hasidic Jews, and after an ultra-Orthodox man was stabbed in Monsey on his way to a local synagogue.

The New York Police Department had already said on Friday that it was stepping up patrols in Jewish neighborhoods after a series of anti-Semitic incidents last week.

The five victims of Saturday’s attack were taken to the hospital, and four of them were treated there and released. By Sunday afternoon, one remained there with a skull fracture, officials said.

That person, according to Abe Rosenberg, captain of Hatzalah E.M.S., the local emergency response service, is elderly and recently underwent heart surgery. “We are praying for him. But a person this age with critical medical condition, anything can go bad,” he said.

Yossi Gestetner, a co-founder of the Orthodox Jewish Public Affairs Council, a group that covers New York and New Jersey, said one of the victims was the rabbi’s son.

On Sunday, members of the Hasidic community said they took some solace in the way people at the Hanukkah party did whatever they could to repel the attacker, with some throwing furniture at him.