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Kangaroos coach Mal Meninga believes Greg Inglis will come back bigger and stronger in 2019 but refused to guarantee he would regain the captaincy after serving his two-match ban.

Inglis was stripped of the Australian captaincy on Tuesday after he was charged the previous day with drink-driving and speeding offences.

Meninga said Inglis was "bitterly disappointed in himself more so than anything else".

"He stuffed up. He has made a poor error of judgement and he has paid the price for it," he said.

With Roosters and NSW captain Boyd Cordner to now captain Australia against New Zealand and Tonga on October 13 and 20 respectively, Meninga said it was "hard to say" whether Inglis would be reinstated as captain once his two-game ban was over.

"I just want to see Greg have a really strong off-season and start the season really well for the Rabbitohs," Meninga said.

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"He will lead Queensland next year and then we will make some decisions at the back-end of next year about who our captain will be.

"I have great admiration for Greg. I highly respect him, love him dearly ... and he was very excited about the role."

Inglis would have been the first Indigenous captain of Australia on a regular basis since Arthur Beetson, although Laurie Daley did lead the Kangaroos for a Test in Meninga's absence in 1993.

"It is something that he has always dreamed of," Meninga said.

Meninga said Inglis understood and accepted the penalty handed down after he spoke with him on Tuesday and conceded that he had been a major part of setting the standards adopted by the Australian side when the "RISE" ethos - standing for respect, inspiration, selflessness and excellence – was instituted.

He added that Cordner was a "terrific leader and a great role model" who would take the job and run with it.

"He was always going to be a leader in our footy team. He has got the 'c' beside his name now ... and there is no greater accolade," Meninga said.

"For him it is a natural progression ... he will handle it really well. He will grab it. He was excited when I told him about it. He was disappointed for Greg as well, because they get on so well."

Meninga said the game had dealt with the Inglis incident the right way.

"We've got on the front foot, solved it quickly and I think that is really important for our game, to be open and transparent with what is happening," he said.

"It is a good lesson for everyone, and Greg has learnt the lesson the hard way."

Meninga flies out of Brisbane on Thursday with the Prime Minister's XIII squad to prepare for Saturday's clash with Papua New Guinea in Port Moresby.