Rather than letting Mr. Madoff remain free on bail and return to his apartment on the Upper East Side of Manhattan, Judge Denny Chin of Federal District Court ordered Mr. Madoff remanded as he awaited sentencing.

He has incentive to flee, he has the means to flee, and thus he presents the risk of flight,” Judge Chin said. “Bail is revoked.”

Some of Mr. Madoff’s victims in the courtroom applauded his ruling.

The 11 counts of fraud, money laundering, perjury and theft to which Mr. Madoff pleaded guilty carry maximum terms totaling 150 years. Sentencing was scheduled for June 16.

Dressed in a charcoal-gray suit, Mr. Madoff, 70, appeared in a downtown Manhattan courtroom packed with journalists, lawyers and some of his victims and, for the first time, described the scope of what was perhaps the largest fraud in Wall Street history.

Mr. Madoff was sworn in and reminded that he was under oath. Noting that he had waived indictment, Judge Chin asked, “How do you now plead, guilty or not guilty?”

“Guilty,” Mr. Madoff responded.

Flanked by his lawyers, Mr. Madoff began to answer questions from Judge Chin about whether he understood the ramifications of his guilty plea, whether he was satisfied with his legal representation and whether he was competent to enter the plea.

At first, Mr. Madoff’s voice was barely audible as he acknowledged the litany of crimes.

“Try to keep your voice up so that I can hear you, please,” Judge Chin said. At one point, Mr. Madoff asked for water.

In recounting how he sustained a 20-year fraud whose collapse erased as much as $65 billion that his customers thought they had in their accounts, Mr. Madoff said, “I believed it would end shortly and I would be able to extricate myself and my clients from the scheme.”

“As the years went by, I realized this day, and my arrest, would inevitably come.”

“I cannot adequately express how sorry I am for what I have done,” he said. “I am deeply sorry and ashamed.”

Although Mr. Madoff admitted to operating what he called “a Ponzi scheme through the investment advisory side of my business,” he said all other aspects of his enterprise, operated by his sons and brother, were legitimate, profitable and successful.

Mr. Madoff’s fraud was a global scheme that ensnared hedge funds, nonprofit groups and celebrities, and devastated the life savings of thousands of people.

Some of them came to court on Thursday to speak during the 75-minute court hearing.

One was Maureen Ebel, who said: “If we go to trial we have more of a chance to comprehend the global scope of this horrendous crime. We can hear and bear witness to the pain that Mr. Madoff has inflicted on the young, the old and the infirm.”

A federal prosecutor, Marc O. Litt, said the government was continuing its investigation and was looking for assets and anyone else who might be criminally responsible.

It remains unclear where the billions of dollars that his victims lost has gone, and whether those victims will ever see any meaningful restitution. Prosecutors have said the government is seeking $170 billion in forfeited assets from Mr. Madoff, apparently representing all the money that ran through Madoff accounts traceable to the crimes.

A court-appointed trustee liquidating Mr. Madoff’s business has so far only been able to identify about $1 billion in assets to satisfy claims.

This week, the government said Mr. Madoff had 4,800 client accounts at the end of November supposedly containing $64.8 billion in customer savings. But the government said Mr. Madoff’s business “held only a small fraction of that balance.”

As Mr. Madoff arrived at the courthouse early Thursday morning, helicopters buzzed overhead and television news trucks lined the street. The day’s events marked a coda in the saga of a man whose name has become shorthand for an entire era of greed and deceit on Wall Street.

With the promise of steady, unwavering returns, Bernard L. Madoff Investment Securities enticed thousands of investors including boldface names like Senator Frank Lautenberg of New Jersey, the Hall of Fame pitcher Sandy Koufax and a charity run by the Nobel Peace Prize laureate Elie Wiesel.

This week, the government offered more details on how Mr. Madoff ran the fraud that had financed his lush lifestyle of a beachfront mansion in the Hamptons, an estate near the French Riviera and yachts in New York, Florida and the Mediterranean.

Prosecutors said that Mr. Madoff concocted an elaborate charade to make it seem like he was running a legitimate investment business when, in reality, “no such business was actually being conducted.” He hired employees with little training or experience and directed them to generate false monthly account statements.

He shuttled millions between banks in New York and London to make it seem as if he was “conducting securities transactions in Europe on behalf of investors when, in fact, he was not conducting such transactions,” prosecutors said. And they said he repeatedly lied to regulators from the Securities and Exchange Commission to cover up his scheme.