ACMA found the listener's comments breached section 1.3(a) of the code.
However,late last year Jones defended himself from the accusations of incitement to violence,saying only 2.2 per cent of his audience was under 29 and the riots were caused by 18 to 29-year-olds.
In a statement,Macquarie Radio Network chief executive Angela Clark dismissed ACMA's findings as"seriously flawed and ill-founded''.
She said 2GB and Jones were opposed to violence and had repeatedly said so on air at the time.
Talkback radio,by its very nature,aired the sometimes controversial views held in the community,she said.
"A broadcaster's use of listener material does not always indicate agreement with that material,''Ms Clark said.
"In this case ... Alan Jones repeatedly urged listeners to refrain from acting on the calls for violence.
"Instead (he) called on the police and state government to ensure a full and appropriate police response to community divisions and tensions and for lawbreakers to be dealt with swiftly by police.''
Other complaints dismissed
ACMA found that comments made by Jones in his December 8 broadcast implied that people of Middle Eastern background were responsible for raping women in western Sydney.
However,ACMA dismissed complaints about other comments aired on December 5,6 and 9.
ACMA will be writing to Harbour Radio shortly about proposed action against the broadcaster.
As to what that measure would be,ACMA was not yet wiling to comment,with spokesman for the watchdog,Donald Robertson,telling smh.com.au a letter would be sent to Harbour Radio Pty Ltd,the parent company of 2GB,and they would wait for a response from the company.
"We'll be seeking some kind of heightened measure,what that turns out to be is really what comes out of that dialogue between us and Harbour Radio,"he said.
ACMA says Jones'broadcasts are the third breach of the vilification provision of the code of practice by Harbour Radio in the past two years,which means ACMA will"move to pursue significantly heightened compliance measures"from the broadcaster,according to release.
In a separate matter,Jones is facing 12 months jail and/or a fine of up to $5500 for naming on air a child witness in a murder trial.
Deputy Chief Magistrate Helen Syme is due to consider penalties,which also apply to Harbour Radio and Nationwide News,on April 20 at Downing Centre Local Court.
This is the second case against 2GB in regards to the Cronulla riots,the first in January this year when ACMA found that comments byThe Open-Line Show host Brian Wilshire had breached broadcast rules against inciting ethnic hatred.
No action was taken as 2GB had ordered on-air apologies and staff awareness training,ACMA said at the time.
- with AAP