Initially caught off guard, Iraqi forces defending Baghdad hit back with artillery, mortar and sniper fire on Monday after US troops thrust into the heart of the city.

As dozens of US tanks rumbled into the city of five million people and entered two presidential compounds on the west bank of the Tigris, the urban warfare that Iraqi President Saddam Hussein promised the invading forces finally began.

But as night fell, the US troops still occupied at least one of the blitzed palaces in the city centre and gave no signs of planning to leave.

"We can see four tanks. They're still there. The soldiers look very relaxed and are walking around inside the compound," Reuters correspondent Samia Nakhoul said.

By midnight, the city had fallen quiet.

Earlier, the white dust of mortar mingled with a sandstorm to cloak the city, obstructing visibility as the thud of artillery and mortar bombs reverberated across the capital, especially toward the west and south.

Republican Guards took positions behind the information and foreign ministry buildings in the city centre, firing rocket-propelled grenades in the direction of the US troops a few hundred metres away.

Artillery shells, apparently Iraqi, crashed into the huge presidential compound on the west bank of the Tigris river, where American tanks took up positions early on Monday.

A Reuters photographer saw other shells, apparently American, landing in the gardens of the luxury Al-Rashid Hotel near the information ministry.

Almost the only people walking the streets were Iraqi soldiers in full combat gear or fighters in civilian clothes.

Speeding ambulances evacuated casualties.

Residents hid indoors to escape the crackling automatic fire and exploding shells. State television showed old footage of Saddam and played patriotic songs.

'Grilling Their Stomachs'

US forces said they captured two presidential compounds in Baghdad, including the main Republican Palace, which has been the target of almost three weeks of US air and missile raids.

The palace complex, stretching several kilometres along the western bank of the Tigris, houses the headquarters of the Republican Guards.

Information Minister Mohammed Saeed al-Sahaf said Iraqi forces were slaughtering the enemy and denied that US tanks had captured the palaces.

"As our leader Saddam Hussein said, God is grilling their stomachs in hell," said Sahaf, standing on a roof in central Baghdad and ignoring US tanks a few hundred metres away across the Tigris.

"Fighting is continuing in the main battlefields. Baghdad is secured and fortified and Baghdadis are heroes."

'Still Some Work to Do'

"The fact that Iraqi forces are still fighting against US forces shows that there is still some work to do," Lieutenant Colonel Peter Bayer, operations officer for the 3rd Infantry Division, told Reuters correspondent Luke Baker.

Two US soldiers and two journalists were killed and 15 people wounded when an Iraqi rocket hit a US communications centre on Baghdad's southern fringe.

In a separate incident, two Marines were killed trying to secure two bridges on the eastern outskirts of the city. Marines told Reuters two of their comrades were killed and three wounded when an artillery shell fired by their own side fell short.

Reuters correspondent Matthew Green said the Marines later secured the bridges and crossed with tanks and armoured vehicles. They then took on Iraqi Special Republican Guard units on the Baghdad side of the river, he said.

The western side of the Tigris, which is called Karkh, was deserted, including a villa complex housing senior Saddam aides.

Iraqi soldiers pointed their rocket-propelled grenades at cars coming over the bridge from that direction. Huge concrete blocks thrown on the bridge offered only a narrow passage.

Symbols of Saddam's power, such as security complexes and the military industrialisation headquarters, lie in the west.

Iraqi television on Monday twice relayed a call to arms from Saddam, which was first broadcast on Sunday.

"President Saddam has issued an order... to all the fighters. If you find it difficult to join your unit for any reason you should join the unit that you can find until further notice."

Seven police cars drove around the centre near the Palestine Hotel where many journalists are staying, with uniformed men honking and firing into the air and waving the Iraqi flag.

"Glory of the Arabs! We will defend you, Saddam, with our blood!" they shouted.

Scores of civilians chose instead to flee the bombardment.

"I think 80 per cent of the people have left to the east to escape bombardment," said Ali, a resident of Saddam City, a sprawling slum on the outskirts of Baghdad.