The attacks come after the Iraqi government asked people living in Falluja to help them capture a man called Abu Musab al-Zarqawi.
He leads a group of Iraqis who don't like the way the country is being run and is thought to be behind the deaths of a number of hostages.
The US military says they are not trying to take control of Falluja.
His group has said they carried out bomb attacks on Thursday inside Baghdad's Green Zone.
That's a part of the city where US forces and the Iraqi government are based and is one of the most heavily protected places in Iraq.
Hear story
Iraq: picture galleries
Chat about the news
Try the Iraq quiz
