She has been missing since around 7pm on Monday when she vanished while playing with friends.
Mr Cameron said the disappearance was "every family's nightmare" and urged anybody who knew anything about it to contact the police.
"My heart just goes out to April's family. This is every family's nightmare, having this happen and the fact that she suffers from cerebral palsy, something I know a little about from my own children, only makes this worse," he said.
"My appeal would be to everyone, if you know anything, if you saw anything, heard anything, have any ideas you can bring forward, talk to the police, help this family find their lovely child."
Police have been given until 5pm tomorrow to question Mark Bridger, 46, about April's disappearance. They were interviewing him again today.
Specialist police search teams are being helped by a marine unit, mountain rescue, the coastguard and lifeboat services.
Superintendent Ian john said the search operation was "one of the largest of its kind in recent history".
Detective Superintendent Reg Bevan also renewed an appeal to the public to come forward with any sightings.
He said they were trying to "piece together" Bridger's movements around the time April disappeared.
He added: "The investigation continues and our focus remains finding April.
"The investigation team will be interviewing Mark Bridger again today and we will continue to piece together his movements during the relevant times and look to overlay his account with that we have gleaned from witnesses, sightings and the other inquiries we are conducting."
Mr Bevan said a "vast" amount of forensic analysis was being carried out, forming a "crucial part" of the inquiry, but this alone would not find the little girl.
"Again I make an appeal to the public to help us find April, and in particular we are looking to trace the movements of Mark Bridger between 6.30pm on Monday and 3.30pm on Tuesday and any sightings of him between these times," Mr Bevan said.
"If anyone has had contact with him during this period, we urge you to come forward."
Police are also appealing for information about his blue Land Rover Discovery, registration L503 MEP.
The Ministry of Defence today stated that Bridger had never been a soldier, as had been reported.
April's family have launched a pink ribbon campaign.
The youngster's godmother Mair Raftree said: "What Coral (April's mother) has asked everybody to do is, if they can, put one on front doors, gates, or to wear a pink ribbon, because that's a favourite colour for April."
She added: "Just anybody, please, wear a pink ribbon."
The mayor of Machynlleth, Gareth Jones, said the bad weather in Wales was hampering the search efforts, which are said to be focusing on six villages in the area.
He said: "Everybody is on hold and there is only one thing on everybody's minds – to get April home safe and sound."
Asked about the mood in the town, Mr Jones added: "It's a mood of worry, anticipation and uncertainty."