U.S. soldiers pushing toward Baghdad advanced through a gap west of Karbala on Wednesday after a night-long bombardment of the strategic city and the first major ground battle against Saddam Hussein's hardcore Republican Guard.

The Army's 3rd Infantry Division launched a heavy attack on towns and positions north of Karbala, where 2,000 paramilitary members of the Saddam Fedayeen and the Baath Party were believed to be hunkered down. The attacks began around midnight Tuesday.

At least 20 Iraqi were killed and an unknown number of fighters were taken prisoner, field reports said. No U.S. casualties were reported.

Karbala is a Shiite Muslim holy city about 50 miles from the Iraqi capital.

Lt. Col. Scott Rutter, commander of the 2nd Battalion, 7th Infantry Regiment, 1st Brigade, said Iraqi troops concentrated their attacks on his battalion, allowing the rest of the brigade to pass through the Karbala gap unscathed.

The gap is a chokepoint between a lake to the west and the city of Karbala to the east. The gap opens onto a plain.

Farther to the east, Marines seized an important bridge over the Tigris River near the city of Kut amid fighting with the Baghdad Division of the Republican Guard, according to a Pentagon official who spoke on condition of anonymity. The bridge allowed thousands of Marines from the 1st Marine Expeditionary Force to cross the river in their push toward Baghdad from the southeast.

Around Karbala, Iraqi defenders fired anti-aircraft guns into the sky most of the night, as artillery pounded suspected military positions in the ancient town. U.S. B-52 bombers circled Karbala throughout the night, carpet-bombing some areas while U.S. Air Force and Navy fighters went after small targets.

Late Tuesday, the Army fought parts of the guard's Medina Division after Tomahawk cruise missiles and airstrikes pounded division positions near Karbala.

Pentagon officials have said the Republican Guard must be eliminated before ground troops move on Baghdad. For more than a week, coalition airstrikes and artillery barrages have pounded Republican Guard units to the south, west and north of the capital.

The Pentagon's top general, Joint Chiefs of Staff Chairman Richard Myers, said the Medina Division's fighting strength had been reduced by more than half. Military officials said the Republican Guard's Baghdad division, centered around the city of Kut to the southeast, also has been similarly worn down.

Myers said elements of two of Iraq's northernmost Republican Guard divisions -- the Adnan and Nebuchadnezzar -- had moved south toward Baghdad, apparently to reinforce units coming under punishing attack from above.

The Karbala fighting took place on one of three south-north routes that coalition forces are using to approach Baghdad, the ultimate prize.

About 100 miles to the southeast, across the fabled Euphrates River, U.S. Marines near the town of Dinwaniyah killed at least 80 Iraqi soldiers and took more than 40 prisoners in an eight-hour battle.

The 3rd Battalion, 4th Regiment came under artillery and mortar fire, and hundreds of Iraqi fighters with rocket-propelled grenades and rifles were said to be inside the town. Marine 155 mm howitzers miles away fired on Iraqi mortar positions, tanks and bunkers.

The Marines killed 80-90 Iraqi fighters, said Lt. Col. B.P. McCoy, and took 44 POWs -- among them Republican Guard officers, recognizable by their red boots. They bulldozed a pit and put barbed wire around it for holding prisoners. Other POWs were taken away in trucks.

Cpl. Patrick Irish of Grants Pass, Ore., described the Iraqi fighters as "shooting from buildings, from dugout positions, from holes, from everything. They would jump out to shoot. They were behind buses -- you name it, they were there."

Other Iraqi fighters turned and ran.

"It looks like a lot of them saw what was coming and changed their mind," said Sgt. James Mares of Chalfont, Pa. "It's just a matter of putting down enough fire until they ran. They died, or decided to give up."

Iraq's defense minister, Sultan Hashem Ahmed, claimed aerial bombardment of Republican Guard positions south of Baghdad had caused minimal damage, because of "good fortifications."

"The Republican Guard Corps are in their best morale and will inflict damage on the enemy that it had never seen before," he said.

He added that coalition forces had failed to capture any towns, because "they never found anyone to cooperate with them."

Iraqi officials also claimed Tuesday that U.S. Apache helicopters had attacked a neighborhood in the central city of Hillah, killing 33 people and injuring more than 300. The U.S. Central Command said it was investigating -- but that no Apaches could have been involved.

In southern Iraq, Marines of the 15th Expeditionary Unit's Echo Company captured a police compound Tuesday evening on the outskirts of Nasiriyah, part of an intense push to gain final control of the key southern city.

The Marines seized the huge, walled compound without any resistance: The site had been abandoned -- a sign that Iraq's stiff resistance in the area may be faltering.

Associated Press reporter Doug Mellgren reported that a column of amphibious assault vehicles slowly rolled up to the compound under a dark, moonless sky dotted with stars. The calm was interrupted when the Marines opened fire on the guard towers that ring the compound. Illumination rounds flashed in the sky to make the targets more visible.

It was the first time some of the troops had fired their weapons.

"Firing at Iraq? It was nice," said Sgt. Robert Renfrow, 28, of Lake Stevens, Wash., who manned a .50-caliber machine gun mounted on an amphibious assault vehicle. Artillery fire pounded the compound, and small grenades were used to knock down the wall that protected it.

Wearing night vision goggles, Marines went from building to building, checking windows and doors to ferret out any hostile Iraqi forces. Two Iraqis were detained.

Also in the south, British troops guarding a key bridge outside of Basra exchanged fire with forces inside the city. Dressed in full combat gear, British forces responded to two mortar attacks, one in the morning and another in the afternoon.

Hundreds of civilians continued to stream out of the city with pickup trucks and automobiles full of personal belongings, food and even livestock. But the exodus had slowed from previous days.

For the first time during the war, a Patriot missile destroyed an Iraqi ballistic missile launched against U.S. and coalition forces in Iraq, the U.S. military announced. It wasn't known what type of munitions the Iraqi missile was carrying.