At the same time, very loud explosions have been heard from the direction of one of Saddam Hussein's presidential palaces.
One US colonel has told reporters some of his men are searching important government buildings and control one of the main palaces.
Troops have faced some fighting back in the city, but many Iraqi soldiers have been seen leaving their firing positions and taking off uniforms.
US troops raided the city on Saturday.
Commanders say they now have most of the city surrounded. This means Iraqi soldiers will find it hard to move in or out of Baghdad because important roads are blocked.