John Clarke and Ross Stevenson, who created The Games, claim the British show is a rip-off of their own successful series which ran over two series in 1998 and 2000.
Clarke and Stevenson claim their production colleague Rick McKenna met with the BBC in 2006 after London had been awarded the Olympics.
McKenna met BBC head of comedy Jon Plowman in London with the idea of re-formatting the series for the UK.
"At a later date,'' Stevenson and Clarke said on ABC website The Drum, "Jon Plowman introduced Rick McKenna to writer John Morton with the prospect that perhaps we might consider John Morton as one of the writers on the project.
"John Morton was lent DVDs of The Games.
"At the time he acknowledged he had never previously seen nor heard of the show and was impressed and keenly interested.
"After many phone conferences, meetings and almost four years of email exchanges, Mr Morton and Mr Plowman have now apparently made a satirical series for the BBC about the organising committee of the London Olympics without our participation or permission.
"In other words, it seems that in 2008/9 Morton had already had the idea he'd never heard of and was so excited by, and he was interested in obtaining episodes of The Games only so he could check out how someone had created his original idea in Australia, 12 years previously.
"We have suggested that once Mr Morton finds out that repressed memory is not an Olympic event, perhaps he could return the DVDs'."
The BBC have claimed that their series, which stars Hugh Bonneville, Jessica Hynes and Olivia Coleman and is narrated by David Tennant, is original.
Its first episode was screened last night on BBC 4 and attracted 341,000 viewers, a 1.75 per cent share of the audience, with another 8,000 on the BBC HD channel at 10.30pm.
"Twenty Twelve is an original and distinctive comedy series looking at London as it counts down the last 1000 days before the 2012 Games begin." the BBC said in a statement.
"It is written by John Morton who created People Like Us and Broken Newsfor the BBC. It's comedy delivered through a distinctively British sense of humour.
"We have investigated the complaints made in relation to The Games and have found no evidence to support the allegations of copying.
"No use has been made of any material deriving from The Games and we are confident that the allegations are without foundation''.
Channel 9, meanwhile, has commissioned a new series of The Games, which will focus on Australia's preparations for London 2012.
March 2011: Mike Rowbottom: Twenty twelve – tasked with making us laugh