An X-ray showed the 5-month-old bird had eaten two $2 coin-sized stones and they were caught in her digestive tract.
Vet was due to perform an endoscopic procedure to remove them this morning.
Happy Feet, who was found on the Kapiti Coast, underwent a similar procedure to remove material from his gut.
If Manukura's stones couldn't be removed through the oesophagus, the bird would undergo invasive surgery.
Dr Argilla said today that the kiwi had passed the smaller of the two stones and the remaining rock would be removed if it stayed caught in her gut.
"The stone still in there is slightly larger but the rock that was passed is not very sharp.''
She said intravenous fluids and a high protein diet would have helped the stone to pass through Manukura and she hoped the second stone would also pass through with the same apparent ease.
She gave the kiwi a 70 per cent chance of surviving surgery, but an infection she had developed could be aggravated if the stone caused abrasions.
"Infection is an ongoing worry because even a tiny tear in the stomach can cause blood poisoning and become fatal.''
Dr Argilla said the procedure was similar to Happy Feet's but on a smaller scale and more challenging.
"It is risky.''
Mr Lester said centre rangers and staff were "relatively confident'' Manukura would survive surgery.
The kiwi had been given anaesthetic for the X-ray and had been since fed a high-protein meal slurry to help build her strength for the operation.
"There is always a danger with anaesthetics and invasive surgery, but death would be certain if we leave the stones where they are now,'' Mr Lester said.
"I would say the risk is relatively low if her strength levels are high. She's in good hands. They're some of the best vets in the southern hemisphere.''
Mr Lester said it was common for kiwis to sometimes eat foreign objects, "but they're usually shiny like nails or screws, and smaller''.
