US Army officials said on Sunday evening that they had encircled Baghdad and established control over all the roads leading to and from the city.
Troops of the 3rd Infantry Division engaged Iraqi troops in the western suburbs of Baghdad and dozens of shorter-range mortar bombs landed in the centre of the city, according to BBC.
US officials also said that the first American military planes had landed at the Saddam International Airport.
Earlier, for the second day on Sunday, elements of the 3rd Infantry conducted reconnaissance missions inside Baghdad, according to CNN.
A US column of 2,000 tanks was also on its way to Baghdad, having crossed the Euphrates River in the morning, according to BBC.
It will join the two brigades [the 3rd Infantry based at the Saddam international airport to the west of Baghdad and a marine force on the southeastern side] that are in position near the capital.
On Saturday, units from the 3rd Infantry fought Iraqi troops in southwest Baghdad, according to reports.
US Central Command spokesman Captain Frank Thorp said more than 2,000 Iraqi soldiers were killed or injured during the mission.
The US Central Command base in Doha, Qatar, said a new strategy was being implemented over Baghdad.
CNN quoted a US official as saying that there would be two aircraft over Baghdad at all times.
When coalition troops need help, the jets would call in at least six aircraft.
Air strikes will be called against missile and anti-aircraft artillery sites and if ground troops are threatened, it said.