The pair have also been documenting their travels on Instagram, where they have 19,000 subscribers.
Two Australian social media influencers have been detained in Iran for taking illegal photos with a drone, according to a source with knowledge of the situation. Separately, another Australian woman is also reportedly being held in the same jail, Evin prison, on unknown charges.
King and Firkin were reportedly camping in a military area around Jajrood, according to The Guardian.
Online followers raised concerns after the bloggers did not post for several weeks.
"Our families hope to see Mark and Jolie safely home as soon as possible", a statement released on behalf of their relatives said.
"We have no further comment to make at this stage and ask that the media respects our privacy at this hard time", they told AAP on Thursday.
The Perth couple jailed in Iran over the alleged use of a drone made no bones about wanting to "wander down the road less travelled".
Mr Firkin is understood to be a construction manager while Ms King is a building designer.
The Australian government is now negotiating the couple's release, The Guardian reported.
Separately, another woman - said to be an academic at an Australian university - was detained past year.
Flying a drone without a permit in Iran is punishable by six months in prison followed by immediate deportation.
Prime Minister Scott Morrison said the Federal Government was treating the issue carefully and was in close consultation with officials.
"They're never issues that are addressed well by offering public commentary on them", he told reporters in Canberra on Thursday.
"I note that in at least one of these cases, that's a view that has been expressed by family members".
Asked about detained Australians, Mr Morrison said the government would "continue to pursue these matters in the interests of the Australians at the centre of these cases".
Australia's Department of Foreign Affairs and Trade said it was providing consular assistance to the detained trio and has urged Australians to reconsider travelling to Iran.
The notorious prison is where Iran holds its political prisoners and has a reputation for the scene of various human rights abuses, including summary executions.
News of the arrests came after Australia announced it would join a US-led mission to protect shipping through the Strait of Hormuz, with tensions high in the Gulf region.