Consumer Reports and the American Academy of Pediatrics are urging for an immediate recall of the Fisher-Price Rock 'n Play sleeper.

The consumer magazine posted a story about its investigation into the popular baby product Monday, three days after the U.S. Consumer Product Safety Commission and Fisher-Price issued a warning advising consumer to stop using the product by three months "or as soon as an infant exhibits rollover capabilities."

The warning applies to all models of the Rock ‘n Play. The government safety commission said in the statement it is aware of 10 deaths since 2015 "after the infants rolled from their back to their stomach or side, while unrestrained. All 10 infants were 3 months or older."

Consumer Reports says its ongoing investigation found that at least 32 babies have died and their work "has turned up deaths of babies even younger than the 3-month threshold cited in the April 5 warning, and go beyond the risk of rollover."

“Based on the deaths and injuries associated with the Fisher-Price Rock ‘n Play, the product clearly puts infants’ safety at risk and should be recalled immediately,” said William Wallace, senior policy analyst for Consumer Reports, in a statement Monday. “All other inclined sleepers should be investigated by the Consumer Product Safety Commission."

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On Tuesday, the doctor's group of 67,000 children’s health providers nationwide issued a statement because of Consumer Reports' investigation and called for stores to remove the product from store shelves.

“This product is deadly and should be recalled immediately,” said Dr. Kyle Yasuda, president of the American Academy of Pediatrics, in the statement. “When parents purchase a product for their baby or child, many assume that if it’s being sold in a store, it must be safe to use. Tragically, that is not the case..”

Also on Tuesday, the government agency said its work "does not stop" with the alert.

"We are investigating other deaths that have occurred in the Rock ‘n Play," the agency said in a statement Tuesday. "CPSC has requirements it must follow for any decisions concerning recalls. If the evidence shows the need for a recall, we will take that step. We continue to work on this very important safety issue."

Fisher-Price general manager Chuck Scothon said in a statement to USA TODAY on Monday that safety of children was the "highest priority."

“The loss of a child is tragic and heart-breaking," Scothon said. "For almost 90 years, generations of parents have trusted Fisher-Price to provide high-quality and safe products for their children, and we work hard to earn that trust every day."

Consumer Reports notes the sleepers conflict with what the American Academy of Pediatrics recommends for safe sleeping, which is putting infants to sleep on their backs on a firm, flat surface in a bare crib, bassinet or play yard.

Friday's joint statement says Fisher-Price has warned consumers to stop using the product when infants can roll over, which for most babies is around 3 months, but "the reported deaths show that some consumers are still using the product when infants are capable of rolling and without using the three point harness restraint."

On Monday, Fisher-Price said in its statement to USA TODAY that it stands "by the safety of the Rock ‘n Play Sleeper" and it "meets all applicable safety standards."

"We continue to work closely with the Consumer Product Safety Commission regarding the safe use of our products, including the Rock ‘n Play Sleeper," Scothon said, noting it is essential that product warnings and instructions are always followed. "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.”

Consumer Reports thinks the government agency needs to go further and should "set strong rules for all infant sleep products, including mandating what medical experts already recommend," Wallace said. "And if products don’t meet the rules, the agency should quickly get them off the market and out of people’s homes, even if they conform to voluntary industry standards."

"It’s totally inappropriate for companies or the CPSC to put the bulk of the responsibility for safety on parents and caregivers – especially when a product indicates it’s safe for routine sleep but really isn’t – or to imply that they’re to blame for tragedies,” Wallace said.

Follow USA TODAY reporter Kelly Tyko on Twitter: @KellyTyko