TV pictures showed buildings on fire and smoke rising from the heart of the city, where government buildings are.
Meanwhile, British Prime Minister Tony Blair has said the Iraq war must not fail.
In a TV speech - his first since the war started - he said if Saddam Hussein wasn't disarmed now the world would regret it.
'Town captured'
British forces have now also joined the invasion and Mr Blair said we have to give them our full support.
There have been reports from the Kuwaiti news agency that an Iraqi border town has been captured.
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