BAGHDAD, Dec. 29 —United States officials have transferred Saddam Hussein to Iraqi custody, his lawyers said today in statements to Reuters and The Associated Press.

The physical hand-over of Saddam was believed to be one of the last steps before he was to be hanged.

"The American side has notified us that they have handed over the president to the Iraqi authorities," Khalil al-Dulaimi, head of Saddam’s defense team, told Reuters.

"They told us the president is no longer under the authority of the American forces and they requested us not to go to Baghdad," he said.

Munir Haddad, one of the judges on the appeals court that upheld Saddam’s death sentence, told The A.P: "Saddam will be executed today or tomorrow. All the measures have been done."

The judge is authorized to attend the execution on behalf of the judiciary. "I am ready to attend and there is no reason for delays," he said.

After upholding the death sentence against Mr. Hussein on Tuesday for the execution of 148 Shiite men and boys in 1982, an Iraqi appeals court ruled that he must be sent to the gallows within 30 days. In Iraq, where the Constitution requires that the Iraqi president and his two deputies sign all execution orders, officials said it was unlikely that legal formalities would stand in the way. The president, Jalal Talabani, had not received the documents by late Thursday.

But a government official familiar with the process said that little objection would be raised if the execution took place almost immediately. “Even if it happens tonight, no one is going to make an issue out of the procedure,” the official said.

Mowaffak al-Rubaie, the national security adviser, said there would be no advance notice of the execution because of fears that any announcement could set off violence. When asked who would be invited to attend the hanging, Mr. Rubaie said: “No television. No press. Nothing.”

He said that the execution would be videotaped but that it was unlikely the tape would be released.

Even with the security fears, there was little appetite among Iraqi officialdom to spare Mr. Hussein for much longer. “I hope the decision should be implemented very soon,” said Qasim Daoud, a former national security adviser. “Sooner is better because it sends a message that we are determined — we want to get ahead step by step to building a new Iraq, and these messages will help.”

Some rights advocacy groups have criticized the haste of the trial and the appeal. Mr. Hussein was sentenced to death on Nov. 5 by a court set up to judge his years in power, and the appeals court handed down its ruling less than two months later. Mr. Hussein, along with two co-defendants, received his death sentence on a case involving only the killings of the 148 Shiites, in the town of Dujail. More cases were pending.

Since the appeals court upheld the death sentences, rumors have swept Baghdad that the Iraqi government would move quickly to put Mr. Hussein to death. Prime Minister Nuri Kamal al-Maliki has drawn protests of political meddling in recent months by suggesting publicly that the former dictator should die at the earliest possible date.

Public pronouncements by American officials have been much more muted, as all formal queries have been referred to the government of Iraq, or G.O.I. in Baghdad jargon.

One American official who works closely with the Iraqi justice system expressed frustration over the criticism that Mr. Hussein’s trial had received. Considering the difficult security situation in a country emerging from a dictatorship — Mr. Hussein’s — the trial has been conducted as fairly as possible by the Iraqis, the official said. “I’m sure they gave it full deliberation and I have full confidence in them,” the official said.

Sabrina Tavernise, Marc Santora and Abdul Razzaq al-Saeidi contributed reporting.