It is also reported that Arthur said captain Michael Clarke had described fellow batsman Shane Watson's influence on the team as "a cancer".
Arthur was earning 400,000 Australian dollars ($363,700) a year and up to 200,000 in bonuses. He was contracted until June 2015 and wanted payment for three years beyond that, estimating his losses to be as much as 4 million Australian dollars ($3.64 million).
"We're disappointed that it's come to this position," Cricket Australia lawyer Dean Kino told Seven News.
"But Cricket Australia is confident in its position on this matter. And I'm sure it'll get resolved in the appropriate fashion."
Arthur said he was unhappy details of the case, which his lawyers confirmed had been filed with the Fair Work Commission (FWC) in Sydney, had been leaked.
"I am extremely upset and disappointed that confidential documents appear to have been given by others to the media," he said.
"The matters raised in my application to the FWC concerning issues within the Australian cricket team are very sensitive, which is why I was at pains to keep them confidential, especially at this time.
"I have kept them confidential, unfortunately others have now made them public. I want to stress how important to me the members of the team were, and still remain to me. The welfare of the Australian cricket team is upmost to me."
The TV station said the documents reveal tension between Clarke and Watson, particularly regarding team discipline.
Arthur was sacked after David Warner punched England's Joe Root in a bar, the latest in a series of disciplinary issues to dog the team.
He added that he felt discriminated against because he was South African and did not understand the 'Australian way'.
Australia, now coached by Darren Lehmann, lost a thrilling first Ashes test against England by 14 runs and start the second at Lord's on Thursday.
($1 = 1.0998 Australian dollars)
(Writing by Mitch Phillips and Toby Davis in London, editing by Pritha Sarkar)
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