Superintendent Ian John said he expected the media to step back and give the community of 2,000 people time to grieve.
Mr John renewed his appeal for "any scrap of information" about the whereabouts of the missing girl.
This community needs some space to come to terms with what's happened and to deal with this in their own way," he added.
Inevitably I think the media will withdraw from this and let people go back to their day-to-day lives.
Mayor of Machynlleth Gareth Jones said it had been an "extremely difficult" week and it was important to give support to those grieving.
It's extremely important that there's support in place for everybody, obviously April and her family and the general community at large as well.
There's still hope for April.
The Machynlleth community came together in prayer in an emotionally charged service in honour of missing April Jones.
Mark Bridger has been charged with the abduction and murder of missing 5-year-old April Jones.