American and other international carriers have cut flights to the socialist-run nation, which required tickets be priced in the local bolivar currency and then made it difficult for the funds to be reconverted into dollars.

American Airlines, which slashed almost 80 percent of its weekly flights to Venezuela last year over the dispute, said in a statement it would offer service between the Venezuelan capital and New York's John F. Kennedy International Airport five times a week, and that bookings could be made immediately.

Airlines have around $3.7 billion from ticket sales trapped in Venezuela because of the country's 12-year-old currency control system, the International Air Transport Association said in June.

"We continue working with the Government of Venezuela to reach resolution on the outstanding amount owed to us (as per our 1Q15 report $644 million)," American Airlines spokeswoman Laura Masvidal said in an email to Reuters.

There currently are no direct commercial flights from Caracas to New York.

Airlines still flying to Venezuela now tend to price their international routes in hard currency, putting them out of reach of most Venezuelans amid an economic crisis that has led to a sharp drop in the value of the bolivar on the black market.

(Reporting by Girish Gupta; Writing by Alexandra Ulmer; Editing by Paul Simao)