Ten days after Australia implemented its $23-a-tonne carbon tax law, the country's competition watchdog said it has received a total of 630 complaints against it.

Still, the Australian Competition and Consumer Commission (ACCC) claimed the number was dismal compared to the thousands of general complaints, tallying more than 8,000 so far, that the watchdog received in the same period.

The complaints, which could still rise in number in the following days, are not totally unexpected.

"The best way to end the complaints is axe the tax," opposition Leader Tony Abbott told reporters in western Sydney on Thursday.

"We always expected there would be some bad apples out there that might be out to no good but I think all in all the numbers so far would indicate the transition has been reasonably smooth," assistant Federal Treasurer David Bradbury was quoted as saying by Yahoo!7 News Network.

Majority of the complaints, according to Michael Schaper, ACCC deputy chairman, came from the energy retailers, as well as the construction, landfill and refrigerant gases sectors.

Twenty cases out of the 630 are being pursued by the watchdog.

"If we come across businesses that are really setting out to dupe consumers ... then we will certainly go after them," Dr Schaper told ABC Radio on Thursday.

''I've been at pains to say that if you make a mistake in your arithmetic ... we're not going to clobber you for that. We're out to get people who are deliberately using the introduction of the carbon price to dupe consumers into accepting a higher price increase than they otherwise would," ACCC chairman Rod Sims told The Age.

Although the number of carbon-related complaints received by the ACCC represented only less than 10 per cent of the total complaints for the past 10 days, the watchdog said it will be doing some definitive action against some companies in the coming weeks.

"There are a number of consumers that clearly still have questions and we are keen to make sure that they get answers," Dr Schaper said.

"If we come across businesses that really are setting out to dupe consumers and they are using the carbon tax as a pretext without any reasonable basis, then we'll certainly go (at) them."

Prime Minister Julia Gillard, upon hearing of the ACCC's release, said 630 carbon-tax related complaints was not an alarming figure.

"If anything the opposition had said about carbon pricing was true ... you would have expected Australians in their millions to be ringing the ACCC and complaining," she told reporters in Townsville.

"I think the story that's telling you here is how ridiculous the (opposition) fear campaign's been."

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