Madoff wore a dark suit, white shirt and a tie and sat at a polished wood table, surrounded by his lawyers. Prosecutors sat opposite them, and the viewing gallery was crowded with onlookers.

Madoff’s lawyer, Ira Lee Sorkin, said the government’s request for a 150-year sentence bordered on absurd. He called Madoff a “deeply flawed individual,” but a human being nonetheless. “Vengeance is not the goal of punishment,” Sorkin said.

But in meting out the maximum sentence, Judge Chin pointed out that no friends, family or other supporters had submitted any letters on Madoff’s behalf, attesting to the strength of his character or good deeds he had done. Madoff was expected to return to his cell at the Metropolitan Correctional Center in Lower Manhattan while federal prison officials determine where he will serve his sentence.

The hearing on Monday marked a climactic moment in the criminal case against Madoff, whose name has become synonymous with greed and fraud. Dozens of photographers and television camera crews from New York to China waited outside the federal district courthouse on Pearl Street.

It will be at least another three months before the judge makes a decision on repaying the victims. Prosecutors requested more time to sift through Mr. Madoff’s records to determine how much was lost and how many people are owed.

The inspector general of the Securities and Exchange Commission is examining how regulators failed for years to catch Madoff. Investment funds that channeled money to Madoff have been sued, and two have agreed to return millions they withdrew before Madoff’s December arrest.