But federal prosecutors, who have filed hate-crime charges, said Mr. Thomas made journal references to Hitler and “Nazi culture” and also repeatedly searched online for information on local temples and on topics such as “why did Hitler hate the Jews.” He also looked for “prominent companies founded by Jews in America,” prosecutors have said.

The death penalty has been prohibited by New York State law since 2007. But in rare cases, federal prosecutors in New York have said they would seek the death penalty, as in the case of Sayfullo Saipov, an Uzbek man charged in a 2017 truck attack that killed eight people on a crowded Manhattan bike path.

It would seem an unlikely scenario in Saturday’s stabbing. Juries have been generally reluctant to sentence federal defendants to death in New York State.

Last month, the Supreme Court said that it would not allow the Trump administration to resume executions in federal death penalty cases after a 16-year hiatus.

Mr. Neumann, who has seven children and many more grandchildren, was slashed three times on his head and was stabbed in the neck, the family statement said.

Mr. Neumann’s arm was shattered in the attack, the statement said, but his condition is so dire that “no surgery has yet been performed on the right arm.”

The four other victims of the attack have all been released from hospitals.

On Tuesday, additional information about their injuries emerged, as well as new details about the man who helped to stop the rampage and then provided crucial information that the police used to locate Mr. Thomas.