A Libyan military spokesman told the BBC that the ship's movements at the port of Derna had aroused suspicion. The oil company rejected this, saying the ship was delivering fuel to industrial facilities there and authorities had been kept informed.
Derna is now controlled by Islamist insurgents - Wikipedia says by Islamic State of Iraq and Levant (ISIL) forces. The Libyan military attacked the port several times last year in an attempt to dislodge them.
Government spokesman Colonel Ahmed Mesmari said the tanker had been targeted because it had failed to submit to an inspection before entering the port.
Colonel Mesmari said the vessel was supposed to dock at a power plant in Derna but instead "took a different route", entering a "military zone".
"We asked the ship to stop, but instead it turned off all its lights and would not respond so we were obliged to strike it. We bombed it twice."
Col Mesmari told Reuters the vessel had been bringing Islamist fighters to Derna. "We had warned any ship not to dock at the port without prior permission," he said.
The National Oil Corporation did not comment on the allegation but said the bombing of the tanker would have a "very negative" impact on oil shipping from Libyan ports.
Libya has been in chaos since President Muammar Gaddafi was killed with western military assistance in 2011.
Numerous insurgent militias govern territory within the country successive governments, based in Tobruk from September, struggling to seize them back, having been dislodged from the capital, Tripoli last year.
"We strongly condemn the January 4 bombing of a Greek-operated oil tanker near Derna," said State Department spokeswoman Jen Psaki.
"The ongoing escalation of violence in Libya against civilian commercial interests further widens a conflict that is fundamentally political," she said.
"The United States remains committed to working with the international community to help the Libyan people establish an inclusive system of government," said Ms Psaki.
Source : HKSG.