Two US aircraft have been shot down over southern Iraq, according to the US military.
There are conflicting reports about the number of casualties
A Black Hawk helicopter came under small arms fire, and an F/A-18 Hornet was hit by a surface-to-air missile, both near Karbala.
It was the first fixed-wing aircraft to be brought down by enemy fire during the campaign.
Further north, Republican Guard units moved early on Thursday to defend Baghdad from advancing US troops, US military sources say.
US ground forces advanced to within 32 kilometres (20 miles) of Baghdad on Wednesday in one of the most dramatic pushes of the war.
There are conflicting reports about the number of personnel aboard the helicopter when it crashed.
Initial reports said seven of the 11 people on board had been killed, while four wounded were rescued. But US Central Command says there were only six people on board.
Shortly afterwards, a single-seat F/A-18 Hornet fighter plane crashed over southern Iraq, Central Command told BBC News Online.
The fate of the F/A-18 pilot - who has not been named - is not yet known.
A statement from Central Command said the armed forces are "committed to accounting for all coalition personnel" - likely an indication that rescue operations are under way.
In other developments:
A US military spokesman said American forces made breakthroughs in two key areas of the southern approach to Baghdad, effectively destroying two of the Republican Guard divisions defending the city.
- 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
American troops repel an Iraqi counter-attack on a key US-controlled bridge over the Euphrates south of Baghdad, the French news agency AFP reports
- 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
"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".
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.
'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.
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.