Wall Street conman Bernard Madoff was led handcuffed to jail Thursday after pleading guilty to tricking thousands of people out of billions of dollars in one of history's biggest financial scams.

Madoff, 70, told a packed New York court he was "deeply sorry and ashamed" for the decades-long scheme and the former chairman of the Nasdaq stock market now looks likely to die behind bars.

He faces a maximum sentence on June 16 of 150 years after pleading guilty to all 11 counts of fraud, perjury and theft. Prosecutors also want to track down an astounding $177 billion they say passed through Madoff's hands.

Judge Denny Chin asked Madoff, wearing a grey suit, dark tie and white shirt, how he would plead.

"Guilty," Madoff replied.

When Chin ignored defense pleas for Madoff to remain free on bail, and ordered him jailed, applause broke out from some of his victims who had gathered in the court room.

But big questions remain over Madoff's possible accomplices and the extent of his theft, and acting US attorney Lev Dassin said prosecutors were still on the case.

"Today is one step in an ongoing investigation," Dassin said in a statement. "We are continuing to investigate the fraud and will bring additional charges against anyone, including Mr. Madoff, as warranted."

One of Madoff's victims, who was allowed to address the court, said there should have been a trial.

"If we go to trial we have more of a chance to comprehend the global scale of this horrendous crime," the woman said. "We will bear witness to the pain that Mr Madoff inflicted on the young, the infirm and the old."

Madoff looked nervous when he first entered the court, watched from the packed benches and via video link by hundreds more people in a separate room.

But he appeared to gather confidence after Chin asked him to recount his crimes, and speaking publicly for the first time since his arrest on December 11, he summarized how he had ensnared his clients.

They believed he was making legitimate investments, when in reality he was running a Ponzi scheme where funds invested by new clients are used to pay fake returns to existing clients.

Millions of dollars worth of investment funds sat in a New York bank account, which he would then dip into when clients said they wanted money back.

"The essence of my scheme was that I represented to clients ... that I would invest their money in common stock. Those representations were false for many years. I never invested those funds in the securities," he said. "Instead, those funds were in a Chase Manhattan account."

He said he was sorry and that he had never intended to perpetuate such an epic fraud, but that when he started out in the 1990s he felt "compelled" to impress important clients with good returns.

"I believed it would end quickly and I would extricate myself and my clients," he said. "This proved difficult and, in the end, impossible."

"I cannot adequately express how sorry I am," he added, saying: "I am here today to accept responsibility for my crimes."

Although Madoff is now a finished man, vast questions hang over the scandal. Prosecutors say they are still trying to trace the money but have warned that the victims may never fully recover their losses.

No one has established just how much money was stolen. Prosecutors say that shortly before his arrest Madoff reported that he was managing about $65 billion, whereas in reality he held only a "fraction" of that amount.

In total, prosecutors say, the government seeks to recover $177 billion from Madoff, something his lawyers call a wildly inflated figure.

Another key question is who else might have been involved.

"He didn't do these crimes alone and I don't understand why conspiracy is not one of his pleas," one of the victims told the court. "Who handled it when he was gone?"

Dassin stressed Thursday that no deal had been done with Madoff that in exchange for his guilty plea, no other charges would be filed against anyone else.

And legal experts say the probe might turn to others, including Madoff's brother Peter, and his sons Mark and Andrew, who worked closely with him. His wife Ruth is about to get her own lawyer, having previously relied on Sorkin.