The guards are defending the capital Baghdad.
Warplanes and helicopters attacked Iraqi positions guarding the southern approaches.
Eyewitnesses say the sound of the raids - a low rumbling accompanied by flashes which lit up the sky - was very different from earlier ones.
That could suggest that American B52 bombers have been dropping huge bombs.
Meanwhile, the Iraqi port of Umm Qasr is now "safe" and ready to receive shipments of aid, said a British commander.
The commander said he hoped the first ship bringing aid would arrive in 48 hours.
Other main points
A second British soldier has died in fighting near Basra in southern Iraq; another British soldier was killed near the town on Monday.
Tony Blair is to meet US President George Bush later this week to discuss the war, say US government officials
President Bush complains directly to Russian President Vladimir Putin that Russian companies have been selling military equipment to Iraq in breach of UN sanctions
President Bush asks Congress for nearly $75bn (£46bn) to meet the cost of the war
The UK government says they will spend £30m on aid for Iraq