The survey of more than 1,500 Norwegians found that 21 percent strongly agreed with the proposal and 22 percent partially agreed, compared to the 44 percent who opposed the measure.
Bjørn Erik Thon, the authority's director, said that he was amazed at how many supported the proposal.
"From a privacy standpoint, this is a bad number," he told Aftenposten newspaper. "It would be a violation of the newborn's privacy that they could be treated as a potential criminal from birth."
He said he worried that police could determine genes or gene-sets that predispose people towards criminality, allowing them to identify potential thieves and murderers while they are still wearing nappies.
"One can easily imagine that such a sample could be stored somewhere. We do not know how you will be able to use DNA in about 10 or 20 years," he said. "Maybe you will be able to look for a terrorist gene or a criminality gene".
Hege Salomon, a lawyer specialising in representing rape victims, has been pushing for hospitals to send genetic material collected from new-borns to a central database which the police should have access to.
"I'm in favour of it as I see that in Norway there are a large number of rape cases and sexual assaults against children and they are not able to find the perpetrators," she told Afternposten.
"It should be both from newborns and also from people coming into Norway."
She downplayed the risk of DNA samples being used to identify potential criminals before a crime is even committed, saying there should be strict legal limits on who has access to the DNA database.