"The people of Ghana have suffered extensively from the crisis," the groups, which all have operations in Ghana, said in an open letter. "Wealthy private lenders must share in the costs of a crisis they helped to create and cancel the debt."
Ghana is expected to miss a $41 million interest payment due on a $1 billion eurobond on Wednesday. The finance ministry said in December that interest payments have risen to between 70% and 100% of government revenue.
"Ghana’s lenders, particularly private lenders, lent at high-interest rates because of the supposed risk of lending to Ghana," the letter said.
"Given that they lent seeking high returns, it is only right that following these economic shocks, private lenders willingly accept losses," it added.
Signatories of the letter, which included Oxfam, Christian Aid, Caritas Ghana, Debt Justice and ActionAid, said the key challenge was to get private lenders to agree to a significant debt cancellation.
"The G20 can help by making clear that Ghana will be politically and financially supported to remain in default on any creditor which does not accept the necessary debt restructuring," they added.
Ghana launched a domestic debt swap plan at the start of December, days before clinching a staff-level agreement with the International Monetary Fund (IMF) for a $3 billion rescue package.
The IMF has said its board will approve the deal only if Ghana undergoes comprehensive debt restructuring.
The deadline to register for what has been dubbed the Domestic Debt Exchange has been extended three times, as authorities struggle to entice bondholders to participate in the program..
Ghana's consumer inflation rose to 54.1% year-on-year in December, driven by rising fuel, utilities and food costs. International reserves have dwindled to less than two months of import cover.