Mohammed al-Dairi made the appeal to the 15-member council after Islamic State militants beheaded 21 Egyptian Coptic Christians, triggering worldwide revulsion and condemnation.
"Libya needs a decisive stance from the international community to help us build our national army's capacity and this would come through a lifting of the embargo on weapons, so that our army can receive material and weapons, so as to deal with this rampant terrorism," the foreign minister said.
Dairi stressed he was not seeking an international military intervention, but that there was no time to lose to equip the Libyan army to confront the emboldened extremists.
As Libya pressed for urgent military aid, UN envoy Bernardino Leon said political efforts to broker a deal on forming a unity government able to address the threat from extremists could soon yield results.
"I am hopeful that a political agreement can be reached soon. The differences between the parties are not insurmountable," Leon said.
Egypt was pushing for a UN resolution easing restrictions on weapons sales to Libya, but Western diplomats expressed reservations, saying a political deal must be the priority.
"While the political solution is an absolute necessity, it is not an alternative to militarily confronting terrorism," Egyptian Foreign Minister Sameh Shoukry told the council.
- Jordan presents resolution -
Acting on behalf of Arab nations, Jordan circulated a draft resolution late Wednesday calling for an end to the arms embargo against Libya's "legitimate" government and directing a council committee to propose ways to cut off weapons deliveries to militias.
Egypt had earlier proposed a naval blockade to prevent arms from reaching the jihadists.
The draft resolution obtained by AFP "emphasizes the necessity to provide support and assistance to the legitimate authorities in Libya... particularly by providing the Libyan government with the necessary security assistance."
It also called on militias controlling Tripoli to withdraw to allow the return of the internationally recognized government to the capital.
Diplomats said negotiations on the draft text were scheduled for Friday but no date was set for a vote.
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The UN embargo was imposed in 2011 when Libya descended into violence after the uprising against Moamer Kadhafi.
Western powers are wary of committing to an easing of the arms ban in Libya, which is still awash with weapons and where rival militias are battling for control of its cities and oil wealth.
A council diplomat said lifting the arms embargo would be tantamount to pouring fuel on the Libyan fire.
Libya has two rival governments and parliaments, one recognized by the international community and the other with ties to Islamists.
A US-led coalition is carrying out air strikes against IS targets in Syria and Iraq, and the foreign ministers from Egypt and Libya lamented a lack of international strategy to address the IS threat in Libya.
Libya's neighbor Tunisia said it too opposed military intervention, instead calling for a political solution.
That echoed a statement Tuesday by the United States, Britain, France, Germany, Italy and Spain that an ongoing UN effort to get Libya's warring sides to agree on a unity government was the "best hope" for peace.
- Islamist threat -
Libya has descended into chaos since the 2011 revolt, with the internationally recognized government forced to flee to the country's east and militias in control of Tripoli and other main cities.
Some militias have pledged allegiance to the Islamic State group, which this week released a video of the gruesome mass beheadings of 21 Coptic Christians.
"We are dealing with a phenomenon that is now becoming a front, stretching from the Middle East to North Africa, covering the Mediterranean region and the Sahel," the Libyan foreign minister told the council.
The country's main militias, including the Islamist-backed Fajr Libya coalition that has declared a rival government in Tripoli and has been involved in the peace talks, have not linked up with IS jihadists.
But Italian Foreign Minister Paolo Gentiloni warned of the threat of such an alliance.
"There is an evident risk of an alliance being forged between local groups and Daesh, and it is a situation that has to be monitored with maximum attention," Gentiloni said, using an Arabic acronym for the Islamic State organization.
The chaos in Libya has contributed to a dramatic increase in the number of migrants attempting to travel across the Mediterranean to Europe.