They said US and UK forces used guided weapons to attack an Iraqi missile base, which is only 100 metres away from people's homes.
Iraqi officials say 14 people were killed, and another 30 injured, when the market was attacked by missiles on Wednesday afternoon.
However, American defence bosses later said they had not fired any missiles or bombs anywhere near the district of the marketplace.
Coalition forces are trying to hurt as few civilians as possible so if this is confirmed this is a big blow to them.
There will be an investigation into the incident.
This comes as coalition warplanes launched a heavy attack on a convoy of Iraqi tanks in the city of Basra.
It's thought the Iraqi troops were either planning an attack to regain some of the captured ground, or they were heading out of the city because of another possible uprising.
There were reports of Iraqi civilians staging an uprising against Saddam Hussain on Tuesday night, but details are still unclear.
Other main points