"Women, children, men and even old people should support the government and go to the oil ports and terminals to liberate them from the criminals and protect their only sustenance," he was quoted by the Libya Herald as saying Sunday.
Libya has struggled to return to a pre-civil war oil production level in excess of 1 million barrels per day.
Rival groups in the east of the country announced early November they declared independence for the region known as Cyrenaica, which hosts some of Libya's key oil terminals. Labor strikes have shut down processing facilities in the west of the country.
The Libyan newspaper reported Zeidan gave strikers a 10-day deadline to end their protests. He said the situation may have long-term consequences on downstream partners like Italy, which relies on Libya for more than 20 percent of its natural gas needs.