Signatories include Sister Alessandra Smerilli, Coordinator of the Economy Taskforce of the Vatican Commission for Covid-19, Prof Isabel Apawo Phiri, Deputy General Secretary, World Council of Churches, Bishop Josiah Idowu-Fearon, Secretary General of the Anglican Communion, and Rev Fidon Mwombeki, General Secretary of the All Africa Conference of Churches.
The letter was sent to the World Bank and IMF ahead of their annual meetings, taking place from 16 to 18 October, when the two institutions are expected to discuss debt relief for poorer nations as part of planning for the global economic recovery.
The World Bank recently warned the pandemic "threatens to push over 100 million people into extreme poverty and is exacerbating inequality throughout the world".
The Church leaders warn of the "devastation" being wrought by the pandemic in poor countries and lament that they are having to spend precious resources on debt repayments instead of fighting Covid-19.
"As our governments do all they can to respond to the pandemic, we witness the ongoing injustice that the money so desperately needed for medicines, personal protective equipment, emergency food supplies and social safety nets is still being diverted to debt repayments," they write.
They call on the institutions to show "courageous leadership" by cancelling debts as "the most immediate way to release the finance required to prevent millions of our sisters and brothers being needlessly pushed into poverty by the pandemic".
"Without the cancellation of debts, there remains a grave risk that developing countries will not have the money so desperately and urgently needed to halt the spread of the virus, to treat people suffering from the virus and to mitigate and recover from the economic and social destruction threatened by the virus," they say.
The letter was coordinated by global NGOs, including CAFOD, Christian Aid and CIDSE.
It echoes a recent call for debt cancellation from Pope Francis "in recognition of the severe impacts of the medical, social and economic crises" faced by developing nations during the pandemic.