A baby boy admitted to hospital is in a critical but stable condition, police said today.
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."
Describing the baby's condition, Mr Jerome said: "He continues to be treated in a London hospital, and his condition is described as critical but stable.
"I would ask that the community's response is focused upon the welfare and the swift recovery of the baby boy. A thorough investigation is under way and our inquiries are continuing."
He concluded: "The overriding message that is being fed back to me through my officers and through the community is one of a community that is united in wishing this baby boy the swiftest and best of recoveries."