Some members of the Iraqi military are disguised as ordinary members of the public, but then open fire on the troops as they get nearer, it's been reported.
There has also been fighting in Iraq's second-largest city, Basra.
UK military officials say some of Saddam Hussein's closest fighters have opened fire on civilians who are trying to flee Basra, which has a shortage of water, food and medicine since the war broke out.
British troops fired on Saddam's men to protect the civilians, the UK military said.
Meanwhile, the first ship carrying aid has docked in the port of Umm Qasr. The British ship Sir Galahad was delayed because mines were found in the sea.
Other main points:
Bombs continued to be dropped on Baghdad during the day, after another night of raids on the capital
Thousands more US troops are moving in to join the battle for the southern Iraqi city of Nasiriya, backed by heavy artillery
The US plans to double the number of troops in Iraq to about 200,000 in the next month, US officials said