Rebel groups in the east of the country, some of which helped topple the regime of Moammar Gadhafi in 2011, in November declared independence for the region known as Cyrenaica, which has some of Libya's key oil terminals.
Zeidan said Wednesday force may be necessary to respond to oil tankers set for eastern rebel ports.
"Any country or company or gang trying to send tankers to take oil from the seized ports [without first working with formal state entities] ... we will deal with them, even if we are forced to destroy or sink them," he was quoted by the New York Times as saying.
Early this week, the regional government in the Cyrenaica region said it would guarantee the safety of foreign oil companies looking to take oil from areas under its control.
Nearly all of Libya's revenues are generated from oil and natural gas sales and simmering conflict has cost the economy dearly.
Libya before civil war erupted in 2011 was producing around 1.6 million barrels of oil per day. The country has flirted with that level since Gadhafi's regime fell but recent production levels have suffered because of internal conflict.