Proposal mooted as commitment to legal and orderly migration.
Cuba was barred from the group in 1962 after it sought the support of the then Soviet Union and Havana has said it is not interested in rejoining the group.
Washington has repeatedly said the US will not support Cuba’s re-entry until it embraces the democratic principles outlined in the group’s charter, halts human rights violations and releases political prisoners.
Al Jazeera’s Latin American editor Lucia Newman says the OAS was long viewed as little more than a forum where the US dictated its will to its southern neighours, but Wednesday’s move marks the first time the US has had to compromise so as not to be isolated in the region.
The move gives the OAS an air of legitimacy and relevance regardless of whether Cuba wishes to rejoin or not, our correspondent adds.
Latin American countries have restored diplomatic relations with Cuba in recent months and also pushed for an end to a crippling US economic embargo.
And since taking office in January, the administration of Barack Obama, the US president, has called past US policies a failure and moved to improve ties with the Caribbean island.
In April, Washington lifted curbs on travel to Cuba, as well as money transfers by Cuban-Americans to relatives there.
It has also announced in the last few days that Cuba had agreed to resume talks on immigration to the US and begin discussions on direct mail links.