Officers would remain at the site overnight, police said, with further searches resuming at first light on Tuesday.
Chief Supt Pete Thorp said: “I understand members of the public are desperate to help, but I must ask that you leave this work to the professional search teams.
“Please do not put yourselves or others in danger by searching in and around water, and if asked to leave by officers, please understand this is for your own safety and to ensure our efforts focus solely on finding Mackenzie.”
He added: “The thoughts of all those involved in the extensive search operation remain with Mackenzie and his family.”