A popular baby sleeper has been linked to several deaths, parents are being warned, and it's possible the toll could be much higher.

A new investigation reveals that many more infant deaths have been linked to the Fisher-Price Rock 'n Play Sleeper than stated last week by American government regulators.

The U.S.-based Consumer Product Safety Commission reported 10 infants have died in the sleeper since 2015, but this week, Fisher-Price told Consumer Reports the number is much higher.

The company said it's aware of 32 fatalities since the product was first introduced a decade ago.

Consumer Reports suggests the government warning doesn't go far enough, based on what it found, and is advising parents to stop using infant reclined sleep products for unsupervised sleep.

The CPSC and Fisher-Price recommends parents stop using the sleeper when babies are about three months old, or when they show an ability to roll over.

Babies died when they rolled from their backs to their stomachs or sides. All were unrestrained, and all were three months or older, the CPSC said.

But Consumer Reports' review found fatalities younger than three months.

"The danger goes beyond the risk of rollovers, and that's why medical experts explain that products like the Rock 'n Play Sleeper should not be used by any infant for unsupervised sleep," said Rachel Rabkin Peachman, Consumer Reports' deputy of special products.

"The American Academy of Pediatrics' safe sleep guidelines state that babies should not be put to bed at an incline because it can increase the risk of suffocation."

"The loss of a child is a devastating tragedy. We will continue to do all we can to ensure that parents and caregivers have the information necessary to create a safe sleep environment for infants," Fisher-Price told Consumer Reports.

The company noted it does not believe any deaths have been caused by the product, saying in many situations a medical condition was identified as the cause of death. Fisher-Price said in other cases, the product was clearly used "in a manner contrary to the safety warnings and instructions."

The Rock 'n Play is still on store shelves because there's no reported defect.

The CPSC told Consumer Reports it is continuing to evaluate the product and investigate whether there is a defect. If evidence suggests it should be recalled, the commission will take that step.

Medical experts say babies should be placed flat on their backs, alone and free of soft bedding, and should not be at an incline, to minimize the risk of accidental suffocation. Incline sleepers do not align with these recommendations, they say.

The Canadian Paediatric Society has similar recommendations, including that babies should sleep on a flat, firm surface, and that soft materials including couches, air mattresses ad pillows are not safe.