The first visit to Shiite Iran by an Australian foreign minister in 12 years follows the framework political agreement reached last month under which Tehran would accept strict nuclear controls in return for the easing of damaging economic sanctions.
Canberra welcomed the progress towards a comprehensive agreement over Iran's nuclear programme in the Lausanne talks between the five permanent members of the UN Security Council -- Britain, China, France, Russia and the United States -- plus Germany.
Bishop said the framework was an "important step towards a final agreement, which will address international concerns about Iran's nuclear programme", but noted many details remain to be addressed, with a final accord due by June 30.
The statement said she would discuss the nuclear issue and other important concerns with Foreign Minister Mohammad Javad Zarif and other Iranian leaders on April 18.
The Australian newspaper on Friday stressed the "great significance of the rare visit" not only on the nuclear front but also with Iran "crucial to hopes of turning back the Islamic State" group, as the Sunni extremists seek to dominate the Middle East.
"The portents for Ms Bishop's visit are promising. Iran is playing a pivotal role in mobilising Shia militia forces, helping the Iraqi army fight Islamic State," the daily said in a editorial.
"Iran's help in fighting Islamic State is pivotal in the context of the conflict between Sunnis and Shiites spreading across the Middle East."
The Australian urged the minister to "leave Iran in no doubt that it must avoid overplaying its hand... Its support for its Shia proxies, such as the Houthis in Yemen, smacks of the Shia hegemony that enrages other Middle Eastern nations."
- Hundreds held in Australia -
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On asylum seekers, New York-based international watchdog Human Rights Watch urged Bishop to "press Iranian officials to address the violations that compel people to flee Iran and to seek protection elsewhere".
Prime Minister Tony Abbott last week announced: "We will be talking to the Iranian government about taking back people who are... Iranian citizens, because they deserve to be in Iran. They belong in Iran."
Refugee advocates say about 45 Iranian asylum-seekers are in indefinite detention in Australia, as they have already had their claims for refugee status rejected but are refusing to go home.
Iran's ambassador to Australia Abdolhossein Vahaji tried to downplay the return of asylum seekers and pushed Bishop's visit as a chance for new relations between the two countries.
"The issue of forced return of asylum seekers to Iran has not been portrayed correctly," he told Iran's Press TV this week.
"It has only served a domestic purpose," he said, adding that asylum seekers would not figure high on the agenda.
Iranians make up 23 percent of the 1,848 people held in immigration detention centres in Australia, according to official figures from late March, and account for many of the 1,707 held on the Pacific island outposts of Nauru and Papua New Guinea.
More than 750 live in the community on bridging visas but are still awaiting the final assessment of their claims for refugee status.
Under Canberra's hardline policy, asylum-seekers arriving by boat are subject to mandatory detention, and since 2013 have been denied resettlement in Australia, even if found to be genuine refugees, and are instead detained on Nauru or PNG.
"This rare visit is a golden opportunity for Australia to demonstrate its concerns for Iranians' human rights," said Elaine Pearson, Human Rights Watch's Australia director.
"Despite hopes for improvements under President (Hassan) Rouhani, repression continues unabated in Iran, leading people to flee to seek asylum elsewhere, including in Australia."