Malpass told Reuters in an interview that 35 of 73 eligible countries were participating in the G20 initiative, which will freeze debt service payments on official bilateral debt through year-end, and more had expressed interest.
The Debt Service Suspension Initiative (DSSI) will free up US$12 billion that countries can use to deal with the health and economic strains caused by the coronavirus, a new World Bank database shows.
Malpass said the pandemic had clearly delivered a "very serious, long-lasting setback" to the global economy that was hitting the poorest countries especially hard.
The relief agreed by G20 members and the Paris Club of official creditors in April was helping, but further steps would be needed to prevent the economic crisis from widening rates of poverty, he said.
He did not endorse calls by African countries and others for an extension of the debt holiday through 2022 and cancellation of some debts, but said further steps would be needed.
"We need to look for ways to provide additional debt relief for the poorest countries and then look at the broader situation facing developing countries," he said.
He also urged the private sector to boost its participation.
"It doesn't really make sense for the commercial creditors to continue taking in, requiring and legally enforcing payments from the ... poorest countries that have been struck by both the pandemic and the deepest economic recessions since World War Two," he said.
Some countries have been reluctant to seek such relief out of concern it could harm their credit ratings and access to international capital markets.
The new database would provide increased transparency about debt levels and creditors, a key step in creating an attractive investment climate to promote future growth, Malpass said.
Eric LeCompte, executive director of Jubilee USA Network, said having the data in one place would make it easier to deal with an impending wave of debt restructurings.
"It's no longer a question of if, now it's just a matter of when," he said.
The G20's International Financial Architecture Working Group is due to meet virtually on June 23 to discuss the initiative and private sector participation, LeCompte said.