Indeed, the sight was so extraordinary, so unexpected – despite all the Pentagon boasts and Bush promises – that one somehow forgot the precedents that it was setting for the future history of the Middle East...

It started with a series of massive vibrations, a great "stomping" sound that shook my room. "Stomp, stomp, stomp," it went. I lay in bed trying to fathom the cause. It was like the moment in Jurassic Park when the tourists first hear footfalls of the dinosaur, an ever increasing, ever more frightening thunder of a regular, monstrous heartbeat.

From my window on the east bank of the Tigris, I saw an Iraqi anti-aircraft gun firing from the roof of a building half a mile away, shooting across the river at something. "Stomp, stomp," it went again, the sound so enormous it set off alarms in cars along the bank.

And it was only when I stood on the road at dawn that I knew what had happened. Not since the war in 1991 had I heard the sound of American artillery. And there, only a few hundred metres away on the far bank of the Tigris, I saw them. At first they looked like tiny, armoured centipedes, stopping and starting, dappled brown and grey, weird little creatures that had come to inspect an alien land and search for water.

You had to keep your eye on the centipedes to interpret reality, to realise each creature was a Bradley fighting vehicle, its tail was a cluster of US Marines hiding behind the armour, moving forward together each time their protection revved its engines and manoeuvred closer to the Tigris. There was a burst of gunfire from the Americans and a smart clatter of rocket-propelled grenades and puffs of white smoke from the Iraqi soldiers and militiamen dug into their foxholes and trenches on the same river bank further south. It was that quick and that simple and that awesome.

Indeed, the sight was so extraordinary, so unexpected – despite all the Pentagon boasts and Bush promises – that one somehow forgot the precedents that it was setting for the future history of the Middle East.

Amid the crack of gunfire and the tracer streaking across the river, and the huge oil fires that the Iraqis lit to give them cover to retreat, one had to look away – to the great river bridges further north, into the pale green waters of that most ancient of rivers – to realise that a Western army on a moral crusade had broken through to the heart of an Arab city for the first time since General Allenby marched into Jerusalem in 1918. But Allenby walked into Jerusalem on foot, in reverence for Christ's birthplace and yesterday's American thrust into Baghdad had neither humility nor honour about it.

The US Marines and special forces who spread out along the west bank of the river broke into Saddam Hussein's largest palace, filmed its lavatories and bathrooms and lay resting on its lawns before moving down towards the Rashid Hotel and sniping at soldiers and civilians. Hundreds of Iraqi men, women and children were brought to Baghdad's hospitals in the hours that followed – victims of bullets, shrapnel and cluster bombs. We could actually see the twin-engined American A-10s firing their depleted uranium rounds into the far shore of the river.

From the eastern bank, I watched the marines run towards a ditch with their rifles to their shoulders and search for Iraqi troops. But their enemies went on firing from the mudflats to the south until, one after another, I saw them running for their lives. The Iraqis clambered out of foxholes amid the American shellfire and began an Olympic sprint of terror along the waterside; most kept their weapons, some fell back to an exhausted walk, others splashed right into the waters of the Tigris, up to their knees, even their necks. Three climbed from a trench with hands in the air, in front of a group of marines. But others fought on. The "stomp, stomp, stomp" went on for more than an hour. Then the A-10s came back, and an F/A-18 sent a ripple of fire along the trenches after which the shooting died away. It seemed as if Baghdad would fall within hours.

But the day was to be characterised with that most curious of war's attributes, a crazed mixture of normality, death and high farce. For even as the Americans were fighting their way up the river and the F/A-18s were returning to bombard the bank, the Iraqi Minister of Information gave a press conference on the roof of the Palestine Hotel, scarcely half a mile from the battle.

As shells exploded to his left and the air was shredded by the power-diving American jets, Mohammed Saeed al-Sahaf announced to perhaps 100 journalists that the whole thing was a propaganda exercise, the Americans were no longer in possession of Baghdad airport, that reporters must "check their facts and re-check their facts – that's all I ask you to do." Mercifully, the oil fires, bomb explosions and cordite smoke now obscured the western bank of the river, so fact-checking could no longer be accomplished by looking behind Mr Sahaf's back.

What the world wanted to know, of course, was the Question of All Questions – where was President Saddam? But Mr Sahaf used his time to condemn the Arabic television channel al-Jazeera for its bias towards the US and to excoriate the Americans for using "the lounges and halls" of Saddam Hussein to make "cheap propaganda". The Americans "will be buried here," he shouted above the battle. "Don't believe these invaders. They will be defeated."

And the more he spoke, the more one wanted to interrupt Mr Sahaf, to say: "But hang on, Mr Minister, take a look over your right shoulder." But, of course, that's not the way things happen. Why didn't we all take a drive around town, he suggested defiantly.

So I did. The corporation's double-decker buses were running and, if the shops were shut, stallholders were open, men had gathered in tea houses to discuss the war. I went off to buy fruit when a low-flying American jet crossed the street and dropped its payload 1,000 metres away in an explosion that changed the air pressure in our ears. But every street corner had its clutch of militiamen and, when I reached the side of the Foreign Ministry, upstream from the US Marines, an Iraqi artillery crew was firing a 120mm gun at the Americans from the middle of a dual carriageway, its tongue of fire bright against the grey-black fog drifting over Baghdad.

Within an hour and a half, the Americans had moved up the southern waterfront and were in danger of over-running the old ministry of information. Outside the Rashid Hotel, the marines opened fire on civilians and militiamen, blasting a passing motorcyclist onto the road and shooting at a Reuters photographer who managed to escape with bullet holes in his car.

All across Baghdad, hospitals were inundated with wounded, many of them women and children hit by fragments of cluster bombs. By dusk, the Americans were flying F/A-18s in close air support to the US Marines, so confident of their destruction of Iraq's anti-aircraft gunners that they could clearly be seen cruising the brown and grey skies in pairs.

Was this what they call "rich in history"? General Stanley Maude invaded Iraq in 1917 and occupied Baghdad. We repeated the performance in 1941 when the former prime minister Rashid Ali decided to back Nazi Germany. The British, Australians and Arabs "liberated" Damascus from the Turks in 1918. The Israelis occupied Beirut in 1982 and lived – not all of them – to regret it. Now the armies of America and, far behind them, the British – a pale ghost of Maude's army – are moving steadily into this most north-eastern of Arab capitals to dominate a land that borders Iran, Turkey, Syria, Jordan and Saudi Arabia.

As night fell, I came across three Iraqi defenders at the eastern end of the great Rashid Bridge.These three – two Baathist militiamen and a policeman – were ready to defend the eastern shore from the greatest army known to man.

That in itself, I thought, said something about both the courage and the hopelessness of the Arabs.