A baby boy admitted to hospital is in a critical but stable condition, police have said.
Candlelit vigils were held in Gravesend on Saturday and Sunday, the second attended by 80 people.
Chief Superintendent Neil Jerome addressed speculation and community unrest over the baby's admission to hospital last Thursday.
He said: "There's been a lot of unhelpful speculation around social media and also what's going on in the community.
"It's our job to establish the facts and to conduct a thorough and professional investigation. "
Mr Jerome played down the significance of the release on bail of a 35-year-old man and 33-year-old woman on suspicion of assault.
He said: "Releasing individuals on bail, for this type of inquiry, is not uncommon.
"Our focus and the focus of the medical professionals is around the recovery of the baby.
"We need to work with them to establish the exact and precise nature of the injuries, and once we've done that we will then be in a position to advance the investigation in its next phase."
When asked about the nature of those injuries, he replied: "It would be absolutely inappropriate for me to go into those details because we are working with the hospital to establish exactly what they are."