The G20 is an intergovernmental forum comprising 19 countries and the EU.
The group's finance ministers and central bank governors met in southern Bengaluru, India, on Thursday on the eve of the anniversary of Russia's invasion of Ukraine.
It was the first of 200 events planned in India this year after the country assumed the presidency of the G20.
“We are also witnessing rising geopolitical tensions in different parts of the world,” Mr Modi said in a recorded video.
"There are disruptions in the global supply chains. Many societies are suffering due to rising prices, and food and energy security have become major concerns across the world."
The financial viability of many countries is threatened by unsustainable debt levels, the Prime Minister said.
“I urge that your discussions should focus on the most vulnerable citizens of the world. Only by creating an inclusive agenda will the global economic leadership win back the confidence of the world,” he added, highlighting India’s G20 theme of one earth, one family, one future.
He urged attendees to bring back stability, confidence and growth to the global economy.
She said the G20 meeting was an “incubator of ideas”, which could transform lives around the globe by leveraging strengths while respecting needs and circumstances.
“Supporting the countries most in need and reflecting the concerns and aspirations of developing countries will be central to our efforts,” said Ms Sitharaman, who will also hold talks with representatives of more than 10 countries, including the US, Italy, Spain, Indonesia and the UK.
She met US Treasury Secretary Janet L Yellen on Thursday and the two leaders exchanged views on G20 Finance Track priorities under India's presidency.
The summits coincide with the first anniversary of Russia’s invasion of Ukraine and come as the US and Europe redouble efforts to impose economic sanctions on Moscow.
Ms Yellen called on member countries to introduce tougher steps against Moscow along with stronger condemnation of the war in Ukraine.
New Delhi has been wary of the West bringing up the Ukraine war at the G20 platforms, according to media reports, after India's government refused to explicitly condemn Moscow over its military invasion.
Moscow and New Delhi have historically been friends.
India has in recent months increased its import of cheap Russian oil despite sanctions imposed by the US.