* Increase reflects buyers taking oil before US sanctions return

* Top destinations for oil were Asia, United States and Europe

* OPEC-member nation rebuilds stocks of Merey 16, diluted crude

HOUSTON/MARACAY, Venezuela, June 3 (Reuters) - V enezuela's oil exports recovered in May from a low figure the previous month as state oil company PDVSA's customers rushed to take cargoes ahead of the resumption of U.S. sanctions on the South American country.

The U.S. Treasury Department in April did not renew a broad license that had allowed Venezuela to freely export its oil, but gave companies until the end of May to complete transactions, including crude and fuel sales. It also began issuing individual authorizations to energy firms doing business with Venezuela.

A total of 50 vessels departed Venezuelan waters last month carrying an average 708,900 barrels per day (bpd) of crude and fuel, and 614,000 tons of petrochemicals and oil byproducts, according to internal PDVSA documents and shipping data from financial firm LSEG.

The volume of oil shipped in May was 30% larger than in April, and 7% above the same month a year earlier. Exports of petrochemicals and byproducts were the highest in 13 months, the data showed.

Over a third of total exports, or 250,000 bpd, were bound for Asia. The United States was the second largest recipient with an average of 205,000 bpd sent by U.S. oil major Chevron to its own refineries and others, followed by Europe with 129,000 bpd.

Shipments to political ally Cuba rose to some 70,000 bpd from 23,000 bpd the previous month, driven by larger crude oil deliveries, according to the data.

Following the completion of maintenance work at some crude upgraders and more imports of diluents, PDVSA's inventories of diluted crude oil rose to almost 5 million barrels. Stocks of the OPEC-member nation's flagship Merey 16 crude also recovered to almost 3 million barrels at the end of the month, one of the documents showed.

Venezuela imported some 68,000 bpd of heavy naphtha and blendstock for producing gasoline, above the 57,000 bpd of April.

Washington since mid-April has granted individual licenses to companies including France's Maurel & Prom, Spain's Repsol and to do oil and gas business with Venezuela. More than a dozen others are waiting for green light.

(Reporting by Marianna Parraga in Houston and Mircely Guanipa in Maracay, Venezuela; editing by David Evans)