"Trust in international financial institutions has eroded. This is partly because they have been slow to reform themselves," Modi said by video link as the two-day gathering began.
"We need to collectively work to strengthen multilateral development banks for meeting global challenges like climate change and high debt levels," he said.
The G20 talks in Bengaluru, India focused on the continuing damaging effects of the Covid pandemic and the Ukraine war, as well as debt relief for poorer nations reeling from high food and fuel prices.
The International Monetary Fund said ahead of the meeting that around 15 percent of low-income countries are in debt distress and an additional 45 percent are at high risk.
The IMF said it was convening in Bengaluru a new Global Sovereign Debt Roundtable to "pave the way for creditors, both public and private, and debtor countries to work together".
The G20's Common Framework for Debt Treatments has so far had limited success, largely on account of disagreements between China and other large creditor countries.
Discussions around green industry financing will be in focus after the European Commission laid out its Green Deal Industrial Plan this month -- a move seen as countering the US Inflation Reduction Act.
Global tax reform could emerge as another point of conflict as plans for a global digital tax remain stalled in the absence of consensus between European nations and the United States.
The remarks echoed calls by others for the World Bank to boost lending and widen its remit beyond tackling poverty, although this has raised concerns that it could lose its top-notch credit rating.
US Treasury Secretary Janet Yellen said on Thursday in Bengaluru it was "critical that they integrate work on global challenges into their core mission to sustain progress on these priorities".
World Bank chief David Malpass this month said he was stepping down in June, a year early.
He had drawn fire for refusing multiple times to say if he believed man-made emissions contributed to global warming.
On Thursday, Washington nominated Indian-American former Mastercard CEO Ajay Banga as his successor, drawing criticism over his corporate background and gender.
"We don't need another World Bank president who will further corporate interests like fossil fuel and industrial agriculture," Friends of the Earth said.
"Nothing in Banga's resume inspires confidence that he will turn the World Bank away from a path of neocolonialism and predation by Global North corporations upon Global South countries," said pressure group the Revolving Door Project.
German Finance Minister Christian Lindner however welcomed the proposal, saying Banga's "resume suggests he can help cooperation between developed industrial nations and developing nations."
It was unclear if delegates in Bengaluru would manage to agree a joint statement, in particular because of differences over the Ukraine war.
Lindner said Germany wanted no weakening of the language used in a leaders' declaration in Indonesia in November which said "most members strongly condemned the war".
"For a year we have been witnesses of this awful war in Ukraine started by Russia. And especially on a day like this, and at an occasion such as a G20 event, we need absolute clarity," he said.