Costa Rica accused Nicaragua of deploying troops inside its territory last month in a dredging operation around a island in the San Juan River that has been the source of friction for more than a century.
In a resolution approved early on Saturday in Washington, the OAS hemispheric forum called for the countries to remove their armed forces from the area and begin talks to resolve their differences.
Costa Rica has no army but allegedly mobilized police forces to the border and asked the OAS to intervene in the conflict.
The Costa Rican government also complained that the border depicted by Google maps was wrong and favored Nicaragua.
Google mappers said in a blog on Friday that they had corrected their version of the border, blaming faulty data from the U.S. State Department that had led to ceding as much as 1.7 miles (2.7 km) of territory to Nicaragua.
The Nicaraguan military officer in charge of the dredging operation denied reports that he had used an erroneous Google map in planning the work, according to local media.