U.S. officials hope to know soon whether Saddam Hussein is dead or alive.

A U.S. Central Command spokesman said Tuesday that "it will take some time" to determine whether the Iraqi dictator was killed on Monday when a U.S. Air Force jet dropped four huge bombs on a building where he was believed to be meeting with other regime leaders.

• Maps: Iraq | Baghdad

Meanwhile, coalition forces continued to maneuver their way into and around Baghdad with little or no resistance.

U.S. officials told Fox News there's a chance they could know as soon as Tuesday whether Saddam is dead. They said some "early indications are positive, but they are very preliminary. But we have reason to be optimistic."

"There's a strong chance we got Saddam and probably both sons," senior U.S. officials told Fox News. The officials said the CIA provided the intelligence that led to the strike.

A single Air Force B-1B bomber dropped two standard versions of the 2,000-pound Joint Direct Attack Munition, known as a GBU-31, and two special "bunker buster" versions on a restaurant.

"We had credible info that indicated there was a regime leadership meeting yesterday," Brig. Gen. Vincent Brooks said Tuesday during a Central Command briefing.

"We've had an opportunity … to attack that particular regime leadership meeting. We believe that attack was effective at causing destruction to that facility."

Earlier, coalition officials said they believed Saddam's top commander in southern Iraq was killed.

In a telephone interview with reporters at the Pentagon, a member of the B-1B crew that attacked the Baghdad target said the Air Force bomber dropped the four bombs within 12 minutes of getting the order to conduct the mission.

Lt. Col. Fred Swan said he and the rest of the crew "knew it was important," and that the airborne air controller who directed the B-1B to its target told him, "This could be the big one."

Battle for Rashid Airport

U.S. forces are fighting for control of a military airport in southeast Baghdad as they encounter pockets of unconventional, and at times intense, resistance throughout the capital area, Brooks said.

The Rashid Airport is in a "militarily significant" area between the Diala and Tigris rivers, Brooks said. Taking the airfield would aid efforts to secure the Iraqi capital -- and prevent the escape of high-ranking Iraqi officials, he added.

A coalition A-10 "warthog" warplane went down near Baghdad. The pilot ejected safely and was recovered near the airport. A Central Command official said it appears that the plane was shot down by an Iraqi missile.

U.S. forces are also fighting north of Baghdad, with small pockets of resistance elsewhere in the capital and east of Karbala. Units of the Army's V Corps remained in the center of Baghdad overnight. Other V Corp units carried out attacks Tuesday morning from the south and north of the city.

Two journalists were killed and at least three others were injured when U.S. forces fired upon their hotel in central Baghdad. The Americans were seeking to retaliate against snipers they said were shooting from the 18-story Palestine Hotel's roof.

The U.S. agreed later not to fire on the hotel, where many reporters are staying.

Earlier in the day, a correspondent for the Al-Jazeera satellite network who previously worked for Fox News was killed when the network's Baghdad office was hit by a coalition bomb.

Iraqi forces -- including special Republican Guard, Fedayeen and Baath Party loyalists, as well as civilian-dressed fighters -- staged a counterattack in the capital shortly after dawn Tuesday, sending buses and trucks full of fighters to overrun U.S. forces holding a strategic intersection.

Within an hour, U.S. tanks retook the intersection. At least 50 Iraqi fighters were killed, and two U.S. soldiers were reported wounded. An estimated 600 to 1,000 Iraqi troops were killed.

"We had a lot of suicide attackers today," said Col. David Perkins of the 3rd Infantry Division. "These guys are going to die in droves ... They keep trying to ram the tanks with car bombs."

Saddam Targeted

The attack on the leadership target occurred in Baghdad's upscale Mansour neighborhood.

American intelligence learned Monday morning of a high-level meeting between senior Iraqi intelligence officials and, possibly, Saddam and his two sons, Qusai and Odai.

"We are certain he went in and we did not see him leave," military sources told Fox News.

U.S. officials told Fox News the regime leaders were discussing how to get out of the city and they were standing within 4-6 meters of each other at the time of the strike. The officials said the location is now a huge crater, and that "whoever was in there is dead."

The site had a bunker/underground emplacement and is near underground tunnels, which could have facilitated an escape route.

U.S. officials also told Fox News that coalition forces came within minutes of getting Saddam several times in the last two weeks, but that he escaped or left locations that were struck minutes later.

Officials are getting more and more helpful information from the Iraqi people every day.

"If Saddam did not slip out, we believe we will get some confirmation soon by way of physical evidence/human remains at the site and by monitoring communications," U.S. officials told Fox News.

Iraqi Information Minister Mohammed Saeed al-Sahhaf made no mention of Saddam's fate to reporters, and rejected any suggestion Iraq would surrender to the coalition forces.

"They will be burnt. We are going to tackle them," he said.

Even before Monday's bombing, Iraq's leaders were finding it difficult, if not impossible, to direct troops and other government loyalists, Pentagon officials said.

"We may not know if or where he is," Defense Secretary Donald H. Rumsfeld said before news of the Mansour strike broke, "but we do know that he no longer runs much of Iraq."

Baghdad Pummeling Continues

U.S. forces continued Tuesday to push into Baghdad from the north and the south as explosions, the thud of shells landing, anti-aircraft and machine-gun fire and the drone of aircraft filled the air.

An Associated Press reporter embedded with a Marine unit in the eastern suburbs of Baghdad said Iraqi fighters were still taking occasional shots at the Marines. He said many of the fighters apparently have taken off their military uniforms to blend in with the civilian population.

Civilians have approached the unit to offer food and cigarettes, but the Marines aren't allowing them to get close for fear of terrorist attacks. The Marines have been told to shoot at any vehicles approaching at a high rate of speed.

State television went off the air around mid-morning. Many residents were hunkered down in their homes. Some civilians went about their business with Kalashnikovs in hand.

Traffic built up toward the north of the city as thousands of people continued to flee the capital. Long lines formed at gas stations. Some ran out of gas and closed; others were taken over by the military.

Uncollected garbage piled up.

"The hostilities phase is coming to a conclusion," Secretary of State Colin Powell told reporters on Air Force One en route to Belfast, Northern Ireland, where President Bush and British Prime Minister Tony Blair were meeting.

He said the U.S. government is sending a team this week to Iraq to begin laying the groundwork for an interim authority.

British forces began establishing the first post-war administration in Iraq on Tuesday, putting a local sheik into power in Basra.

The sheik had met British divisional commanders Monday and been given the job of setting up an administrative committee representing other groups in the region.

Fox News' Rita Cosby, Ben Johnson, Carl Cameron, Bret Baier, Ian McCaleb, Major Garrett and The Associated Press contributed to this report.