Detectives across Britain are joining the hunt for a girl aged about three or four who was seen being put into the boot of an estate car on Wednesday.
Shoppers at Sainsbury's saw the girl being put into a car
Police say there may be an "innocent explanation", but they are becoming increasingly anxious about her welfare.
Shoppers at a Sainsbury's store in Swansea saw a man put the child in a Hyundai Lantra estate at 2145 BST.
The car - registration N729 FOO - had been seen in London a day earlier and headed back to England on Wednesday.
South Wales Police said there had been no reports of missing girls of a similar age in their area.
The force is now working with the Metropolitan Police and Avon and Somerset Constabulary, as well as neighbouring Welsh forces.
The girl was partially clothed and apparently asleep or limp, police said, when a white, slightly built man with blond, straight hair was seen placing her in the back of the blue or green Hyundai.
He was aged between 30 and 50 and was the driver, they said.
Witnesses also described seeing a front seat passenger. He was between 30 and 50, over 6ft tall and of heavy build with a beer belly and light, short hair.
Police believe the green or blue car comes from London or England's Home Counties
They have also confirmed that the licence number it is reported to display is not registered to anyone.
Late on Wednesday it crossed the old Severn Bridge into England, heading towards the M4 motorway.
A spokesman for the south Wales force said officers were becoming increasingly concerned for the girl's safety and "desperate" to trace the driver.
He said: "The incident took place late at night and it looked very unusual to see a young girl being put in the back of the car."
Det Supt Paul Kemp, who is leading the inquiry, said on Saturday that officers had received calls from members of the public who had provided information.
But he added: "We are yet to hear from anyone that can positively tell us the whereabouts of this car and its owners.
"I would ask anyone who has seen the car or know of its whereabouts to come to speak to us as soon as possible."
Earlier, Det Sup Kemp had said the incident could be an "entirely innocent occurrence".
He added: "At this current time, and until we receive information to prove the contrary, I have grave concerns for the welfare of the young girl."
Police said they had been dealing with one main witness to the events, who they describe as "credible".
She was a shopper who followed the car for a short distance along Fabian Way out of the city before telephoning the police.
Officers can be contacted on 01792 456 999 or Crimestoppers anonymously on 0800 555 111.