Expert teams have been combing areas of thick forest in the mountains around the town of Machynlleth, where she disappeared on Monday.
Police have until 17:00 BST to charge or release Mark Bridge - suspected of abducting April - although they could apply to hold him for longer.
They are searching a small farmhouse in the nearby village of Ceinws where he was known to be living most recently.
Search teams began lifting up paving slabs outside the property while activity continued inside.
Mr Bridger, 46, was arrested on Tuesday and is being held at Aberystwyth police station.
His dark blue Land Rover Discovery was seized by detectives for forensic examination.
On Thursday police renewed an appeal over Mr Bridger's movements - saying they were keen to piece together where he had been from 18:30 BST on Monday to 15:30 BST on Tuesday.
At a news conference Superintendent Ian John, of Dyfed-Powys Police, gave details of the search operation that is going on.
"We are utilising eight specialist police search teams led by five specialist police advisers with the support of the national police search centre," he said.
Supt John also praised the public's response.
"Following the appeals for information that we've made, we've received over 2,500 calls from the public," he said.
"All these calls need to be answered and that's being done by all 44 police forces around the country.
"I'm sure you can imagine the operation that's going on in and around our force area to process that information and make sure that everything is being given to the right priority."
He also praised the hundreds of people who had volunteered to help with the search, gathering at the local leisure centre each day.
"I've had the privilege of going over there and thanking them for the support they're giving in this difficult operation.
"I also want to turn to April's family," he said.
"I'm sure we're all feeling for them at this terrible time - also the friends and extended family."
April's mother has made a plea for people to wear pink ribbons to support the search.
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Meanwhile a special area has been created in the foyer of April's school to show its support.
The school, Ysgol Gynradd Machynlleth, said after a request from April's mother all pupils created small individual heart-shaped messages.
The school has also set up an open book for parents, pupils and staff to leave "messages of support for April, Coral, Paul, Jasmine and Harley during this traumatic time".
Hundreds of local people responded to a fresh call for people living within a 10 to 15 mile (16-24km) radius and with a good local knowledge of the area, to contact rescue coordinators.
They are currently searching areas around 32 villages, concentrating initially on 15 communities.
Dyfed-Powys Police have asked anyone with information to contact a dedicated hotline on 0300 2000 333.
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