The NRL was on Wednesday continuing a review into Katoa's three head knocks at Eden Park, which left him suffering seizure activity and a brain bleed.
The 25-year-old was given an oxygen mask and rushed to hospital during Tonga's loss to New Zealand at Eden Park on Sunday, before requiring surgery.
Katoa's uncle Reverend Setelo Katoa told radio station PMN Tonga on Wednesday his nephew's status had progressed in an Auckland hospital.
With Katoa speaking in Tongan, PMN host John Nicholas Pulu translated the news to English.
"We've got some great news about the state and health of Eliesa Katoa, who was in ICU," Pulu said.
"He has moved into a different part of the hospital where he is recovering at the moment."
"They are very grateful for the prayers and support of everyone.
"Not just Tongans, but many, many people from various countries and communities who have been showing love and support.
"They ask for continuous prayer and support that he will make a full recovery.
"What beautiful news we have received this afternoon."
The Katoa update came as questions linger over how the forward was allowed to play after copping a head knock in the warm up on Sunday.
Tonga officials remain adamant they did not see vision of Katoa's warm-up collision until after the match.
Replays of the incident, captured by broadcasters, showed Katoa falling backwards to the ground after teammate Lehi Hopoate's shoulder struck him in the head.
The 25-year-old then suffered two further hits to his head in the game, and while he passed a HIA for the first of those the Melbourne star fell ill after the second.
Under current rules clubs have spotters at training looking for head knocks, while all contact sessions must be videoed to allow any hits to the head to be reviewed.
An independent doctor in the bunker also watches all contact in games to identify head knocks, with trainers also at the ground to check head contact.
But as it stands there are no such measures required for pre-game, with Katoa's sickening collision with Hopoate the first noted warm-up incident of its kind.
New Zealand coach Stacey Jones on Wednesday backed calls for more surveillance of warm ups.
"There should be scrutiny around it," Jones said.
"I don't know what went on ... but there has got to be some real good care around the players."We have it at training.
"But again I don't know enough to comment what went on.
"My thoughts and prayers are really just with Eli right at the moment ... Obviously it wasn't nice and I just hope for Eli to make a full recovery."
Jones's comments come after fellow Kiwis great Shaun Johnson said earlier this week "heads will roll" over the incident, furious Katoa was allowed on the field.
Katoa's former teammate at the Warriors, Jazz Tevaga, said the situation should "never have happened".
"It's very heartbreaking to see for my brother Eli," Tevaga told AAP at Samoa's fan day ahead of Sunday's Pacific Cup final against New Zealand.
"I sent him a message and pray he is okay.
"It shouldn't have happened, but it did happen. All we can do is pray and hope he comes through the other side."
Katoa's former teammates and Kiwis players Isaiah Papali'i and Charnze Nicoll-Klokstad were among others to throw their support behind Katoa on Wednesday.
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