Rowhani, secretary of Iran's Supreme National Security Council, is lined up for talks with Australian Prime Minister John Howard, Foreign Minister Alexander Downer and other officials.
IRNA said only that the talks would focus on "mutual, regional and international issues", but the visit comes several weeks ahead of a key International Atomic Energy Agency (IAEA) meeting on Iran's nuclear programme.
Iran is stepping up its diplomacy ahead of the September meeting of the UN's nuclear watchdog, hoping to counter an effort by the United States -- which accuses Iran of seeking nuclear arms -- to see the Islamic republic referred to the UN Security Council for possible sanctions.
Tehran says it is merely trying to generate nuclear energy and insists on its right to master the entire nuclear fuel cycle -- something that could later be transformed into a weapons programme.
Downer visited Iran in May 2003, when he said "it would be unacceptable if Iran was to move towards the establishment of a nuclear weapons capability".