Updated

Two more cards have fallen from the deck of the U.S. military's 55 most wanted (search)  Iraqi fugitives.

Saddam Hussein's former interior minister and a top member of his Baath party (search) are now in the coalition's custody, U.S. Central Command said Wednesday.

Mizban Khadr Al Hadi (search), a high-ranking member of the Baath Party regional command and revolutionary command council, and Mahmud Dhiyab Al-Ahmad (search), the former interior minister, are now in the hands of the U.S. military after being taken in two unrelated incidents, according to a statement from Tampa, Fla.-based Centcom.

Al Hadi, No. 23 on the U.S. list of most wanted fugitives from Saddam's ousted regime, turned himself in in Baghdad, while Al-Ahmad, No. 29, was captured.

"Coalition forces will continue to work at apprehending former members of the Saddam Hussein regime," a Centcom statement said.

Thirty-four of the 55 people on the most wanted list are now in custody, but not Saddam or his sons Qusai and Odai.

But their time on the run may be limited. Senior Defense officials told Fox News that U.S. troops were following up on "new and promising leads" in the hunt for Saddam and his sons.

Gen. Tommy Franks (search), who turned over his position as U.S. war chief to Gen. John Abizaid (search) on Monday, said on Good Morning America that it could be a "just a matter of days" before the United States gets new leads on the top three's whereabouts.

"The noose is tightening quickly," one senior defense official told Fox News.

Just before the war began, al-Ahmed was named commander of one of four military regions for the defense of Iraq. He held a news conference just after the war began wearing a bulletproof vest and brandishing an assault rifle.

"Some of you may be wondering why I am dressed like this," he said at the time. "Well, because we in Iraq have pledged not to relinquish our guns until the day we are victorious."

The U.S. Army's V Corps reported that Hadi was arrested in early May, but that information was incorrect, said Maj. Brad Lowell, a Central Command spokesman.

The previous arrest occurred June 17, when Abid Hamid Mahmud al-Tikriti (search), Saddam's top aide, surrendered after informants' tips led U.S. forces to his hideout in Saddam's hometown, Tikrit.

The U.S. military recently offered a $25 million bounty for Saddam, and a $15 million reward for each of his two sons. Following these offers, two more recordings purporting to feature the voice of Saddam himself turned up on Arabic television channels.

On Tuesday, U.S. soldiers raided a building in central Baghdad, following up on a claim by residents that say they thought they saw Saddam driving through the area on Monday, and say the ousted leader was met with cheering and gunfire by supporters.

Several pro-Saddam residents chanted pro-Saddam slogans on Tuesday as the U.S. servicemen conducted their sweep, with some singing: "With our souls and our blood we sacrifice ourselves for you Saddam."

The last verified sighting of Saddam came April 9 in the Azamiyah neighborhood of northeastern Baghdad as the capital fell to U.S. troops.

L. Paul Bremer, the top U.S. official in Iraq, said Tuesday that the coalition would not rest until Saddam's fate was determined and reassured Iraqis that he would never again rule their country.

"He may be alive, but he is not coming back," Bremer said. "I think the noose is going to tighten around his neck. His days in Iraq are finished."

Meanwhile, insurgents in Fallujah, a restive town west of Baghdad, fired two rocket propelled grenades at American troops. The U.S. military and police in Fallujah said there were no injuries and no arrests made.

Iraqi police Lt. Iyad Abed said one of the two grenades exploded in the air and the second landed on the street outside a U.S. base in central Fallujah (search), 35 miles west of Baghdad. The Coalition Press Information Center said there were no injuries or damages.

Witnesses said two U.S. helicopters flew over the site soon after the early morning attack.

The Qatar-based Al-Jazeera satellite station reported a second skirmish in Fallujah, when a U.S. patrol came under fire. The station also reported a 10-minute gunbattle early Wednesday between U.S. troops and unidentified gunmen farther west in the town of Ramadi. The U.S. military in Baghdad said it had no information on the reported incidents.

On Wednesday, the U.S.-led occupational government also announced it would begin recruiting members of a new Iraqi army on July 19. Maj. Gen. Paul Eaton, in charge of the new recruits, said the coalition hoped to have 1,000 soldiers training by August, and 12,000 by the end of the year. They hope to have 40,000 by an unspecified date in 2004.

And another American has died in Iraq.

The soldier, attached to the 101st Airborne Division, died Monday from what the military said was a non-combat gunshot wound near Balad, 55 miles north of the capital. The soldier's name was withheld pending notification of next-of-kin.

Attacks on U.S. forces in Iraq have been taking place virtually every day, likely carried out by pro-Saddam loyalists and Iraqi insurgents. But Bremer and other officials are standing by Washington's assertion that the violence does not amount to a full-fledged guerrilla war.

Bremer blamed the attacks on remnants of Saddam's Baath party, former members of pro-Saddam militias and terrorists. He acknowledged that some of the attacks, like the fatal shooting of a U.S. soldier at Baghdad University on Sunday, showed "professionalism."

Seven U.S. soldiers were wounded in and around Baghdad on Tuesday, while the U.S.-led provisional authority announced a $2,500 reward for information leading to the arrest of anyone who kills a coalition soldier or Iraqi police officer.

U.S. defense officials, meanwhile, revised upward their count of Americans killed by hostile fire in Iraq since the war began in March to 143, a figure that approaches the 147 killed in the 1991 Gulf War.

Fox News' Bret Baier and The Associated Press contributed to this report.