Cleary on Tuesday was fined A$4,000 (£2,100), with another A$6,000 (£3,150) suspended, by the NRL after he was seen in a photograph with a group of women sitting on his lounge at home in defiance of public health orders aimed at containing the coronavirus.
The 22-year-old apologised in an interview with local broadcaster Channel Nine late on Tuesday, saying the women were his sister's friends and had popped in to his house for 10 minutes while waiting for an Uber.
New videos emerged on Wednesday of Cleary dancing with the women, calling into question his account.
“I messed up, I spoke to the integrity unit about what happened but they didn’t ask me about the TikTok videos, they just asked me about the pictures and I’ve already told them about that,” Cleary said on Wednesday.
“I wish I hadn’t done the video, just got carried away in the moment. I was stupid. I messed up.
“I’m just finding the whole social distancing and isolation stuff too much. It’s not something anyone has ever gone through before, it’s difficult.
“I regret doing the video. If they fine me more I’ll deal with that at the time. I’m just going to wait and see what happens when I speak to the integrity unit.”
Australia's New South Wales state, where Cleary lives, is still under a strict lockdown to contain the virus, with people banned from having anyone in their homes besides those who live there on a permanent basis.
Cleary was one of four players fined by the NRL on Tuesday and given suspended one-match bans for social distancing breaches.
The four included two Australian rugby league internationals, Latrell Mitchell and Josh Addo-Carr, who were charged by police with firearms offences while on a camping trip in rural New South Wales over the weekend.
The breaches have been hugely embarrassing for the NRL, which has been at pains to convince authorities it can safely restart the season on 28 May.
The season was suspended after two rounds in March due to travel curbs making it untenable.
A slew of Australian lawmakers have criticised the players, and Queensland-based senator Matthew Canavan said the NRL sanctions dealt to the players were not heavy enough.
“These guys are knuckleheads for doing what they’re doing,” Canavan said.
"There are hundreds of staff at football clubs being laid off over the last couple of months and they’re putting all of that at risk with this behaviour."
Australia has reported more than 6,700 cases of Covid-19, with 88 deaths.
Because of the actions of Cleary, Mitchell and Addo-Carr, as well as Newcastle Knights squad player Tyronne Roberts-Davis, who was also fined A$1,000 (£520) by New South Wales Police after a gathering with several others over the weekend, the season is in danger of not being restarted, according to state Premier Gladys Berejiklian.
"We always base any decision on health advice and on the ability of an organisation to stick to that health advice so I think it does jeopardise, what's happened, because the season hasn't even started,” she said.
"Ordinarily people might turn a blind eye here and there but not when it's life and death. We are in a pandemic. It's life and death. To compromise someone else's safety, that's inexcusable."
"The word disappointing doesn't really cut it, does it?"
The NRL said in a statement on its website: "Our players are role models and we expect them to lead by example during this pandemic.
"On face value, the image in today's media is both disappointing and an unacceptable breach of health orders."
Berejiklian made it clear that more was expected from the players.
She said: "Everybody's trying so hard to stick to the rules, everybody's trying so hard to do the right thing and then to have people behave in that way is beyond belief.
"There are a number of question marks and the organisation doesn't do itself any service by having players acting that way."
Reuters and PA
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