Several people have been visited by police after they made threatening remarks toward family of a young boy injured in a suspected case of abuse in Flaxmere.

The case of the 4-year-old boy who was found badly bruised and suffering from a severe head injury in his Flaxmere home on January 29 has sparked upset across the country with many people targeting the boy's family.

A local woman took to Facebook on Friday to say she had been visited by a police officer who told her the boy's immediate family had filed a complaint about something she had written.

"He advised me to refrain from putting up any more threatening comments or I'd pretty much get myself into trouble" she said in the post.

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She said she was unapologetic and vowed to continue to speak out.

STUFF The Flaxmere house in which a four-year-old boy sustained critical injuries.

A police spokeswoman confirmed on Sunday that "a small number" of individuals who had made online threats had been spoken to by police.

"No one has been arrested or charged at this stage," she said.

"Police understand that the distressing nature of this incident has caused upset and concern in the community. However we ask people to allow police to continue their work and urge against any speculation or action which may have the potential to impact these enquiries," she said.

"The investigation into this incident is ongoing. We are engaging well with extended family but continue to ask anyone with information to come forward and speak to us," she said.

Information provided by community members was assisting police and a number of officers were dedicated to the investigation and were making progress, the spokeswoman said.

AP People who made online threats to the family of an injured Flaxmere boy have been visited by police. (File photo)

Earlier this month Stuff learnt it was not the first time the boy had been the victim of suspected abuse.

He was admitted to hospital on at least one other occasion, with injuries including broken bones.

Newsroom reported after the first incident in June 2019, the boy was placed in the care of his grandmother in Auckland but Oranga Tamariki returned him to his immediate family in Flaxmere before Christmas.