Antonio Guterres told the General Assembly that polluters should pay for the impact of climate-related events. This question of who funds these losses has long dogged international negotiations.
Poor countries say the rich should pay because of their historic carbon emissions.
But richer nations reject any calls for compensation. Arguments over this question are likely to dominate discussions at the forthcoming COP27 summit in Egypt.
As world leaders gather for the UN General Assembly in New York this week, there's no shortage of critical issues on their agenda. From the war in Ukraine, to food and energy shortages and cost-of-living crises, "a global winter of discontent" is on the horizon, according to Mr Guterres.