NOC spokesman Mohamed El Harari said the state-run Sirte Oil Co would have to shut down its production of 43,000 barrels per day (bpd) if the protest by state oil guards continued, without being more specific about timeframe.
Harari said he did not know what the demands of the guards were. He said Brega port used to export oil but recently had been mostly used to supply the western Zawiya refinery.
Last week the government managed to negotiate an end to a protest blocking the 340,000-bpd El Sharara field in the southwest. A rebel group also agreed to restart the eastern Ras Lanuf and Es Sider ports they had seized almost a year ago.
The protesters at Brega are members of the petroleum facilities guards (PFG), a force made up mainly of former militia fighters who helped oust Muammar Gaddafi in 2011.
The government in Tripoli has tried to co-opt the militias by integrating them into state forces such as the oil guards, but has been unable to control them with its fledgling army, which is still in training.
Members of the PFG often seize oil facilities they are supposed to protect to press the central government to meet political and financial demands, part of growing turmoil in the North African country.
Libya used to produce 1.4 million bpd until July 2012, when a wave of protests started. Its current output is 350,000 bpd, following the restart of the El Sharara field, NOC said on Thursday.
Disputes over Libya's oil resources have been among the many triggers for conflict between rival brigades of former rebels and allied political factions since the 2011 civil war ended four decades of Gaddafi rule.
Since then, Libya's government and outgoing parliament have struggled to rein in militias and impose order, not just in the oil sector. It is unclear whether parliamentary elections last month will finally bring greater stability and security.
On Thursday, the United Nations said it had evacuated dozens of foreign staff from its mission in Libya, prompted by a deteriorating security situation.
The U.S. State Department on Saturday expressed worry about the situation in Libya and urged that the new parliament be seated as soon as possible.
"The United States is deeply concerned by the ongoing violence in Libya and dangerous posturing that could lead to widespread conflict there," spokeswoman Jen Psaki said in a statement, without referring to specific actions.
"Libya's future will not be secured through force of arms but only through a political accord and national dialogue that allow the state to ensure security and rule of law throughout the country," she said.
© Thomson Reuters 2014