Ali Zeidan said that orders had been issued to arrest the tanker's crew.
Earlier separatist militants said they had started loading oil on to the tanker at Sidra port, east of Tripoli.
The rebels have seized three major ports since August, to demand more autonomy, hampering the government's ability to revive oil exports.
The Morning Glory docked at Sidra port earlier on Saturday, after a failed attempt to dock on Tuesday.
A local TV station showed footage of the rebels holding a ceremony to celebrate.
"We started exporting oil. This is our first shipment," a rebel spokesman said.
Libyan officials said the rebel move was an "act of piracy".
Analysts have said it is unlikely the ship is owned or controlled by Pyongyang.
Lawrence Dermody, a researcher in illicit trafficking for the Stockholm International Peace Research Institute, told the BBC: "It's much more likely that it's a flag of convenience," adding that "it's really not a common flag - even in the Middle East."
Libya's state-owned National Oil Corp (NOC) had warned tankers against approaching the port, and two others in Libya's volatile east that are also controlled by armed groups.
It is not the first attempt to ship oil from the rebel-controlled port.
On Monday the Libyan navy ship Ibn Auf fired warning shots at a Maltese-flagged oil tanker to prevent it from docking and loading oil.
The owners of the ship complained it was fired on in international waters.
Libya's government has tried to end a wave of protests at oil fields and ports, which have slashed vital oil revenues, but there has been little progress in indirect talks between the government and former militia leader Ibrahim Jathran, who is now leading the protests.
Libya is struggling with armed groups and tribesmen who helped topple Muammar Gaddafi in 2011 but who have kept their weapons.
The BBC's Rana Jawad in Libya says Mr Jathran's demands include an independent commission representing the three regions of Libya. He wants the commission to supervise the sale of oil and ensure the east gets a fair share of the revenue.
Libya's oil output has slowed to a trickle since the protests started in July last year, depriving the OPEC producer of its main budget source.
Libya's prime minister has threatened to bomb a North Korean-flagged tanker if it tries to export oil from a rebel-controlled port.