The International Monetary Fund (IMF) has agreed to write off the $3.3bn (£1.89bn) owed to it by all but one of the 20 poorest countries in the world.
Nineteen nations stand to benefit from debt relief early next year
It has delayed granting debt relief to Mauritania until it makes "satisfactory progress in a few policy areas".
The write-off follows the Group of Eight debt forgiveness deal which was struck in July.
Earlier this month it was feared the IMF was set to withhold help for up to six of the poorest countries.
Debt-relief campaigners ended up warning some intended recipients that the IMF was set to drop them from the list because their macroeconomic policies did not meet its requirements.
On Wednesday, the IMF dismissed reports that it had been back-tracking as "simply not true".
The multilateral debt relief initiative was agreed by leaders of the G8 industrialised states in July after the series of "Live 8" rock concerts drew attention to the issue.
The debts owed by the 19 nations will finally be cancelled once the IMF has the approval of all 43 rich countries that have contributed to an anti-poverty trust set up by the Fund.
"So far we have 37 consents. We're quite hopeful we'll get remaining the six in the next few weeks," said IMF spokesman Thomas Dawson said.
COUNTRIES APPROVED FOR DEBT WRITE-OFF
They should receive IMF debt relief by early 2006.
Mauritania, meanwhile, is likely to meet the criteria for the write-off "relatively soon", said Mr Dawson.
"Mauritania will qualify for relief and receive it once it demonstrates satisfactory progress on some policy areas that have been identified," he said.
Oxfam, one of the organisations that feared the IMF would go back on its word, welcomed Wednesday's board verdict.
"It's good that the IMF realised that they couldn't wriggle out of promised debt cancellation during a closed-door session in Washington DC," a spokesman said.
"The IMF must now deliver the funding quickly and without any further delay."