On Thursday, the US 3rd Infantry Division was said to have closed to within a few miles of the Iraqi capital, pushing up from the south-west.
Surprise has been expressed at the lack of opposition met by US troops
But reporters with it say it has not been encountering any sizeable resistance.
"The numbers against the Americans were not that significant," said the BBC's Gavin Hewitt.
The Iraqis did seem to have been surprised by the speed of the US advance, he added - but he thought it premature to say that the Republican Guard divisions expected to defend the capital had been overcome.
He had not seen large numbers of destroyed vehicles or prisoners.
BBC correspondent Rageh Omaar, in Baghdad, said the surprise there was that it still seemed to be an open city - with no checkpoints, troops or tanks on the main arterial routes.
Moving around the city he said the picture was of many different forces - regular army, paramilitaries and militias in small units all over the place, but no armour.
"It does not have the appearance at all of a militarised city.
"Something for me just simply does not add up," he said.
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