The Times said a blogger who had been traveling in Asia with her Australian boyfriend, as well as an academic who had studied at Cambridge University and was lecturing at a university in Australia had been detained in separate incidents.
The Department of Foreign Affairs and Trade (DFAT) said three citizens - two of whom also hold United Kingdom passports - have been detained.
Australian citizens have always been advised to reconsider plans to travel to Iran because of a "risk that foreigners including Australians could be arbitrarily detained or arrested".
She and her boyfriend had been arrested about ten weeks in the past as they travelled in Iran throughout a visit they'd been running a blog on social media.
A file photo of Erin Jail in Tehran where the Australian women are reportedly being held.
The newspaper also reported that the academic is in solitary confinement after she was sentenced to ten years in prison for an unknown offence.
Ten-year terms are routinely given in Iran for spying charges.
"More people are being taken and the government needs to do a better job at protecting ordinary people from being held and used as chess pieces in this way", he told Sky News.
Former Foreign Office minister Alistair Burt told BBC Radio 4's Today programme: "Iran does work on a basis of putting the pressure on these countries that it believes are hostile to it. Obviously, we feel that the government should be making it much more costly for Iran to be doing this".
Her husband, Richard Ratcliffe, said: "Our hearts reach out to the families involved. It is a bad situation to be involved in".
They are being held in the same prison in Tehran where a British-Iranian aid worker, Nazanin Zaghari-Ratcliffe, has been jailed since 2016 on spying charges, the Times said.
British police detained an Iranian oil tanker - the Adrian Dayra 1 - in Gibraltar in July, before Iran retaliated by capturing the British flagged Stena Impero on the Strait of Hormuz.
A few weeks later Iran seized a British oil tanker for alleged marine violations, Reuters reported. Seven of the Swedish-owned vessel's 23-strong crew members have since been released.
Australia has advised its citizens to "reconsider your need to travel" to Iran, the highest warning on a four-tier scale after "do not travel" to a country.
The ladies are regarded as the primary British passport holders with out dual-Iranian citizenship to have been jailed within the nation for a number of years.
"The Department of Foreign Affairs and Trade is providing consular assistance to the families of three Australians detained in Iran".
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