The consumer watchdog says it is investigating reports that COVID-19 rapid antigen tests are being sold at excessive prices, but it has not yet seen evidence of widespread price gouging.

The federal government asked the Australian Competition and Consumer Commission (ACCC) to monitor for price gouging following several incidents of individual rapid antigen tests being sold for several times their regular price.

ACCC chair Rod Sims said the watchdog was now investigating, but so far he had not seen systematic price gouging.

"It's very early … at this stage, we've done our own web searches and seen excessive pricing, but the most excessive pricing we've seen so far is [individuals] on eBay, Kogan," Mr Sims said.

He said the ACCC would contact eBay about the rapid test price gouging it had seen, and expected they would help to remove the listings.

But Mr Sims indicated it was unlikely the ACCC would pursue court action against price gougers in the first instance, saying the watchdog had more success in threatening to "name and shame" businesses.

"Clearly we're dealing with a problem here of limited duration … therefore we need to get those prices down now," he said.

However, Mr Sims said that reports of businesses opening multi-test kits to sell the individual tests at marked-up prices were "appalling behaviour" that the ACCC would be "very interested" in pursuing.

He noted that in the middle of a pandemic, such behaviour could constitute unconscionable conduct and result in court action.

Like masks and toilet paper, rapid tests being stockpiled

Rapid antigen tests have been difficult to find since cases of COVID exploded across the country last month and the kits became part of the official testing regime.

The government has been accused of failing to prepare for a predictable rise in demand for rapid tests.

Mr Sims said it was not clear to him whether there were supply issues, or whether the shortages were similar to previous rushes during the pandemic, such as for masks and toilet paper.

"When you're in a pandemic it's awfully tricky," Mr Sims said.

"I remember in the early days of the pandemic dealing with the toilet paper issue .… obviously people were stockpiling it, and there's an issue with stockpiling at the moment.

"Clearly demand is outstripping supply, how much that is due to freight and logistics, how much is due on the demand side to stockpiling, I just don't know."

More than 84 million rapid tests have been ordered by state governments for the coming weeks, which the federal government hopes will sate demands.

The government has urged anyone with evidence of what they believe to be excessive pricing of rapid tests to report the business to the ACCC.

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