His last American concerts came in February 1979, when he visited New York, Boston, Philadelphia and Washington during the administration of President Jimmy Carter, when U.S.-Cuba relations experienced a slight thaw in nearly a half century of frigid ties.
Rodriguez's office said his U.S. visa had not been approved, but the New York concert has already been scheduled for June 4.
The 63-year-old Rodriguez is a staunch defender of the Castro government and has for decades penned politically charged lyrics, though many fans are more moved by his poetic love songs.
In May 2009, Rodriguez wanted to travel to New York for a tribute to another folk legend, Pete Seeger, at Madison Square Garden, but couldn't because U.S. authorities didn't process his visa request fast enough.
Rodriguez is one of Cuba's most famous singers and a founding member of the "Nueva Trova" movement, which mixed music with revolutionary politics. He has for decades filled auditoriums across Latin America and released about 20 albums.
Last month, Rodriguez surprised many by releasing a new album with lyrics suggesting that removing the "r" from "revolution" would lead to much needed "evolution."
"Revolution" in Cuba is a reference to the uprising that toppled dictator Fulgencio Batista and brought Fidel Castro to power 51 years ago.
Though political relations have not significantly improved between Cuba and the United States under President Barack Obama, cultural exchanges involving artists and musicians have become far more commonplace.
Puerto Rico's Calle 13 openly criticized U.S. policy during a March concert in Havana and American funk and R&B pioneers Kool & the Gang came to Cuba in December. A number of top Cuban musical favorites have played Miami and other U.S. locales in recent months, including Salsa stars Los Van Van, pop duo Buena Fe and folk singer Carlos Varela.
ANNE-MARIE GARCIA, Associated Press Writer