US ground forces have beaten divisions of elite Iraqi troops to bring them within 32 kilometres (20 miles) of the Iraqi capital, according to American military officials.
US commanders say the advance has been swift
They are said to have made breakthroughs in two key areas of the southern approach to Baghdad, effectively destroying two of the Republican Guard divisions defending the city.
"The dagger is clearly pointed at the heart of the regime and will remain pointed at it until the regime is gone," said Brigadier-General Vince Brooks at US Central Command in Qatar.
Iraq has denounced the American claims of victories and advances as "lies".
In other developments:
- Arabic broadcaster Al-Jazeera says it will suspend the work of its correspondents in Iraq indefinitely after the Information Ministry bans two of them from working
- US marines appear to be in control of most of the southern city of Nasiriya, a key crossing point on the Euphrates river and the scene of heavy fighting last week
- Iraqi television shows footage of President Saddam Hussein smiling and laughing with members of his cabinet; it is not clear when the pictures were taken
- King Abdullah of Jordan condemns the killing of Iraqi civilians and stresses that his country has consistently refused to open its airspace to US-led forces in Iraq
Correspondents travelling with the forward US forces say they have been moving fast but may have met lighter resistance than they expected from the Republican Guard units protecting the capital.
The BBC's Gavin Hewitt, with the US 3rd Infantry, says commanders believe they have beaten the Medina division of Saddam Hussein's elite troops, although there are concerns that some of the soldiers may have withdrawn to continue the fight nearer Baghdad.
US commanders are anxious to avoid having to fight in Baghdad's streets, where civilian casualties could be high and where Iraqi soldiers would have the advantage of local knowledge.
The push by the US 3rd Infantry through the gap between the town of Karbala and a lake is said to have been part of a three-pronged attack which also saw American marines further east secure a key bridge across the River Tigris near Kut.
The Marines are said to have destroyed the Baghdad Division of the Republican Guard.
'Matter of hours'
Iraqi units have been attacked from the air ahead of the arrival of ground troops.
Raids by B-52 bombers on tanks defending Baghdad included the first ever use six new precision-guided "cluster" bombs, the US military said.
The 1,000-pound (454 kg) CBU-105 bombs each contain 10 armour-destroying bomblets.
BBC defence correspondent Paul Adams, at US Central Command in Qatar, says the American-led forces could be "a matter of hours" from entering the Iraqi capital.
But our correspondents in Baghdad say residents continue to go about their daily business and the atmosphere in the centre is not one of a militarised city.
Statements read on Iraqi television on Wednesday evening said the US-led advance had been halted and that a number of coalition soldiers had been killed and their vehicles destroyed.
HUMAN COST OF WAR
US: 46 dead (including 12 in non-combat accidents, 2 under investigation), 15 missing
UK: 27 dead (including 16 in non-combat accidents, 5 to 'friendly fire')
Iraq: At least 677 civilian deaths, military deaths unknown
*Figures from each government
Iraq's Information Minister Mohammed Saeed Sahaf rejected the US claims of progress.
"They lie every day," he told a press briefing. "Therefore what they say or allege about success and advances in Najaf and Karbala are illusions."
He added: "They also said they crossed the Tigris, which is another lie. As is what they said about Kut."
Iraqi television carried comments by the commander of the Baghdad division - which the US says it destroyed - saying only 17 of his men had been killed and 35 wounded.
Defence analysts say each Republican Guard division would have about 8,000 soldiers.