Orangutans, gibbons, crocodiles, turtles and exotic birds were among the species housed in the artificial habitat designed to mimic a southeast Asian environment.
Zoo staff were working to account for all species held at the attraction after the blaze tore through the plastic material covering the enclosure on Saturday.
All the mammals had been located in the hours after fire broke out, but keepers were yet to track down the rest of the residents.
Attempting to trace all the animals, which included birds, would take “some time”, officials said.
The zoo, which plans to open on Sunday, said it had been inundated with messages from people asking how they could lend their support.
“We remain committed to our mission to prevent extinction and for those who’re asking how they can help, we would welcome a donation to our continuing conservation work,” the zoo said.
A JustGiving fundraising page had received more than £8,000 in donations on Sunday.
Cheshire Fire and Rescue Service declared a major incident after it was called to the zoo shortly before 11.30am on Saturday.
Eyewitnesses described how visitors to the attraction – billed as the largest indoor zoo exhibit in the UK – were rushed to safety as the blaze spread rapidly through the polymer roofing material.
Meanwhile zoo staff led the animals housed in the structure to safety as firefighters arrived on the scene.
One person was treated for smoke inhalation as a result of the fire, according to North West Ambulance Service.
One eyewitness, David Clough, 50, who lives across the road from the zoo, said high winds fanned the flames in the roof of the building.
“We were very worried for the people and animals that would have been in the building,” he added.
“Orangutans and gibbons are our nearest neighbours there, but there are many other animals, including free-flying birds.”
A visitor, who declined to be named, said: “We were in the monsoon enclosure when it happened and were rushed out due to an electrical fire. It spread very quickly.
“The staff ensured all the members of the public were safe. Many staff were running towards the fire, I’m assuming to help with evacuating animals.”
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