More meetings are on the anvil during the remaining days in Australia and Fiji, where he will be making a day-long visit.
It was a warm hug for Australian Premier Tony Abbott by Modi described by the Australian media as a "standout shake" so far at the G20 summit -- that was distinct from the formal handshakes with the host by other world leaders.
Dressed in a black bandhgala suit, Modi narrated an anecdote to President Obama and Abbott during the G20 retreat, sharing with them the story of Chicago-based Walter Burley Griffin, the well known American architect who designed the new Australian capital Canberra and who was buried in Lucknow.
"The life of Walter Burley Griffin is a common link among USA-Australia-India which the leaders appreciated," External Affairs Ministry Spokesperson Syed Akbaruddin tweeted.
Obama and Russian President Vladimir Putin were also seen having a chat with Modi at the summit of the Group of 20 industrialised and major emerging economies.
"Focus on global issues," External Affairs Ministry Spokesperson Syed Akbaruddin tweeted about this interaction.
On the fifth day of his foreign visit, Modi met French President Francois Hollande, Canadian Premier Stephen Harper and Crown Prince Salman bin Abdulaziz Al Saud of the Kingdom of Saudi Arabia.
The Spokesperson, while giving details of these meetings, said Modi had informal interactions with several world leaders, including Abbott, Obama and Prince Saud, during the course of the summit.
The informal meeting of the five-nation BRICS also saw Modi having interactions with Chinese President Xi Jinping, Brazilian President Dilma Rousseff, Putin and South African President Jacob Zuma.
Modi is due to meet German Chancellor Angela Merkel and Spain's Premier Mariano Rajoy tomorrow.
Australian daily The Age while referring to Abbott-Modi hug: said, "The stand out shake so far has been India's Prime Minister Modi, who gave Abbott a hug. An 'awww' could be heard across the media centre. There were no hugs from Abbott besties David Cameron and Stephen Harper. We repeat, no hugs."
Abbott also joined in the tweet exchanges when he made a mention of barbeque lunch hosted by him during the retreat at the Queensland Parliament House.
The Australian leader posted a photo of Modi sharing a lighter moment with Obama and himself during the retreat.
"The BBQ lunch with @narendramodi and @BarackObama was an opportunity for #G20 Leaders to talk in a relaxed atmosphere," Abbott posted.
Modi kicked off his bilateral diplomatic engagements on the margins of the back-to-back India-ASEAN and East Asian summits after he landed in Myanmar capital Nay Pyi Taw, holding several meetings.
Besides his interaction with the summit host and Myanmar President U Thein Sein, Modi met his counterparts from Malaysia, Singapore, Thailand -- Najib Razak, Lee Hsien Loong and Prayut Chan-o-cha -- respectively, and Sultan of Brunei Hassanal Bolkiah.
Modi also met Russian Prime Minister Dmitry Medvedev, Chinese Premier Li Keqiang, Indonesian President Joko Widodo, and Laos Premier Thongsing Thammavong.
In Brisbane, Modi earlier met European Commission Chief Herman Van Rompuy and British Premier David Cameron shortly after his arrival in Australia.