RIO DE JANEIRO—Organizers of the Paralympics, the world’s showcase tournament for disabled athletes, are working to plug financial holes that could lead to service cuts and missing teams at this year’s event, set to be held just after the Olympic Games.

The Rio 2016 Organizing Committee, responsible both for the Olympics and the Paralympics, is late in paying out support grants that teams use to pay for travel to the Games, the International Paralympic Committee said Saturday. Beyond that, an IPC spokesman said the committee...