Modi, who was in Myanmar capital Nay Pyi Taw, left for Brisbane, Australia after attending the ASEAN-India summit and the East Asia Summit on November 12-13.
At the East Asia summit, Modi asserted that the world community must reject any linkage between religion and terrorism while formulating a "genuinely international" partnership in the fight against all forms of terror acts.
On India-ASEAN relationship, Modi said there were "no irritants" in their ties and they can be "great" partners.
He said there will be "major improvement" in India's trade policy and environment and proposed a special facility for speedy implementation of connectivity projects with the 10-nation ASEAN bloc.
On the sidelines of the summits, Modi met Chinese Premier Li Keqiang, Malaysian counterpart Najib Razak, Russian Premier Dmitry Medvedev, and Thai counterpart Gen Prayut Chan-o-cha.
At the G20 summit in Brisbane, Modi is expected to voice his concerns over "jobless growth" in his interventions, stresssing that economic growth should also create employment.
The G20 looks to meet a two per cent increase to its combined growth over five years through economic reform and infrastructure investment. It accounts for 80 per cent of world trade and 85 per cent of global economic production.
After the summit, Modi will proceed to Sydney, Canberra and Melbourne during the course of his bilateral visit from November 16 to 18.
Modi will be the first Indian Prime Minister to visit Australia since Rajiv Gandhi in 1986.
During his stay in Australia, Modi will hold talks with Prime Minister Tony Abbott in Canberra.
This will be the second meeting between the two leaders after Abbott visited India last month.
Abbott will host a reception for Modi at the iconic 161-year-old Melbourne Cricket Ground (MCG). Modi will also address a joint sitting of Federal Parliament.
Modi will travel to Fiji on a day-long visit on November 19 before returning home the next day. He will be the first Indian Premier to visit the south Pacific Island nation after a gap of 33 years, the first being Indira Gandhi in 1981.