Witnesses say the abductors were wearing Iraqi commando uniforms and carried Iraqi military IDs.
The investigation is ongoing, and police are continuing to search for the abductor or abductors.
He set a deadline for the abductor, or abductors, to call the dedicated line by midnight the next day.
This was indicated by the way the abductors got into the house and their "conduct... during that whole operation", he said.
Alerts work, in part, because the vast majority of abductors act impulsively.
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The source said the abductors were demanding that members of their group being held prisoner be released and sent to northern Mali.
"I would say none of these abductors have psychotic breaks, " she said.
The parents paid the ransom without informing the police, having believed the abductors threat to kill their child if the police were involved.
On Saturday, the Arabic-language network Al-Jazeera broadcast video of the hostages with their abductors giving the initial 48-hour deadline for their demands to be met.
It was not clear whether that activity represented "mopping up and checking" or "something more active" being carried out by Algerian forces against the abductors, the official told CNN.
Warren Richard Rodwell was brought to police by residents of Pagadian city who saw him walking before dawn near the fishing port, where his abductors dropped him off, said local police chief Julius Munez.
According to Reunite, a charity that works to put parents in touch with their children when a father or mother has taken them abroad and defied court rulings, Pakistan is the most popular destination for abductors.
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