As of this evening, the Americans had conducted 58 raids in the past 24 hours in the Tikrit region, double the pace of the day before, and military officials spoke with renewed confidence that they had picked up a fresh trail of Mr. Hussein's whereabouts, exactly one week after soldiers killed his sons Uday and Qusay.

The stepped-up hunt for Mr. Hussein coincided with an Arabic-language television station's broadcast of an audiotape that the station said was apparently by Mr. Hussein, in which he mourned his sons and called on fellow Iraqis to take revenge on the American occupiers.

American military officials welcomed the tape, saying that if it proved authentic, the broadcast was an admission by Mr. Hussein that his sons were dead. Many Iraqis have expressed skepticism that the brothers were killed. 

An American military spokesman said that in one raid, soldiers seized four men described by intelligence sources as important members of Mr. Hussein's former government, one of whom was believed to be a longtime bodyguard to Mr. Hussein. The others were suspected of being midlevel security and military leaders. The Associated Press, whose reporters accompanied the soldiers on the raid, identified an Iraqi man seized today as Adnan Abdullah Abid al-Musslit, and quoted commanders as saying he was one of Mr. Hussein's most trusted bodyguards. The man is said to be a cousin of Mr. Hussein's with detailed knowledge of his hiding spots.

A military spokesman said tonight that American soldiers got the men they were looking for and were busy questioning them to determine whether they were the important officials they had originally believed. The official said this evening that interrogations of the men had so far failed to yield any useful information. 

Still, the scale and intensity of the raids reflected the growing confidence among American officials that United States forces were rapidly closing in on Mr. Hussein. 

Military officials here and in Baghdad have said that the deaths of Mr. Hussein's sons prompted many ordinary Iraqis to offer information about Mr. Hussein. As a result, the tempo of military operations has accelerated. 

With checkpoints set up at regular intervals throughout a broad swath of territory north of Baghdad, the Americans were hoping they would squeeze Mr. Hussein in a tightening ring. 

"What we are trying to do is raise the pressure to force him to make a mistake, to get him to travel between location and location, and to nab him that way," said Capt. Jeff Fitzgibbons, a military spokesman in Baghdad. 

In an interview Monday night, Deputy Secretary of State Richard L. Armitage echoed the confidence expressed here, saying American forces had nearly captured Mr. Hussein in a raid Monday near his home.

"We believe we were just hours behind Saddam Hussein," Mr. Armitage told CNN.

American military confidence has increased notably since the deaths of Mr. Hussein's sons in a shootout in the northern city of Mosul. While those deaths did not prove to be the crippling blow to the Iraqi insurgency that was originally predicted by military officials, they said the death or capture of Mr. Hussein himself could prove far more effective at demoralizing his fallen government's remaining supporters in Iraq.

The prospect, however remote, that Mr. Hussein could return to power colors much of the interaction between American officials and the Iraqis, some of whom are terrified that they will pay a price for cooperating with the occupation force. 

So far, 50 American servicemen have been killed in attacks since May 1, when President Bush declared an end to major combat operations. American officials are convinced that the bulk of the attacks, though perhaps not organized, are carried out by Iraqis still loyal to Mr. Hussein. During a stop today in New Delhi, Gen. Richard B. Myers, chairman of the Joint Chiefs of Staff, called the area between Tikrit and Baghdad "still a war zone." 

The voice on the tape released today was halting and raspy, sounding much like the ones on tapes released previously. 

"I mourn to you the deaths of Uday and Qusay and those who struggled with them," said the voice on the tape, broadcast by Al Arabiya television. "You are the honor of this nation. America will be defeated." 

In Baghdad, the vendettas that followed Mr. Hussein's fall from power continued to play themselves out. Today, the police were investigating the death of a former dean of Baghdad University shot dead on Sunday night.

The former dean, Dr. Muhammad Abdullah Falah Alrawi, had been a senior member of the ruling Baath Party and one of Mr. Hussein's personal physicians. A colleague said Dr. Alrawi had been shot by a man who arrived at his Baghdad clinic complaining of abdominal pain. As soon as the man met the doctor, he drew a gun and shot him in the head. 

Dr. Alrawi's son said his father had resigned his university post because he knew that the American policy of purging Baath Party members from important posts would have prevented him from keeping his job. 

No one has been arrested in the shooting, but friends and relatives of Dr. Alrawi said today that the killing was probably linked to his activities in the Baath Party and his presumed influence in the former government. 

"Anyone in the Baath Party is a target," said Dr. Alrawi's 21-year-old son, Yasir.

Also in Baghdad, the 25-member Iraqi Governing Council intended to serve a preliminary Iraqi government announced today that its chairmanship would rotate monthly among nine of its members. Members of the Council said they hoped the rotation would help foster a consensus on major decisions. 

"This way the chairmanship will carry political weight and street credibility," said Nabil Musawi, a deputy to Council member Ahmad Chalabi.