The 15-member council began considering a proposed resolution that would allow Operation Sophia to intercept vessels suspected of transporting weapons to Libya.
The draft resolution prepared by France and Britain would build on a previous measure that gave the EU naval force UN backing for its mission to combat migrant-smuggling.
"We ask this council to adopt a resolution on authorizing Operation Sophia to enforce the UN arms embargo on the high seas off the coast of Libya," EU foreign policy chief Federica Mogherini told the council.
Mogherini expressed hope that council members would "once again do the right thing and make the Mediterranean a safer place, starting for our Libyan friends."
Operation Sophia's enforcement of the arms embargo would help shore up the UN-backed national unity government by cutting off the flow of weapons to the various militias.
Established in Tripoli more than two months ago, Libya's unity government has been trying to unify violence-ridden Libya and exert its control over the entire North African country.
Libya is awash with weapons with 20 million pieces of weaponry in a land of six million people, said UN envoy Martin Kobler.
"These weapons do not fall from the sky, but come in increasingly through illegal shipments by sea and by land," Kobler told the council.
"These shipments must end if there is to be any serious hope of bringing peace to Libya."
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- Russian concerns -
Russian Ambassador Vitaly Churkin said Moscow is not opposed to expanding the mandate of the EU naval operation to include halting arms-trafficking, but he expressed concerned about the response from various Libyan sides.
"Our concerns is that everything must be done in a way that does not create any suspicion against any party," said Churkin.
The draft resolution obtained by AFP invokes Chapter 7 of the UN charter, which allows for the use of military force.
It would grant a 12-month mandate to allow EU vessels to "inspect, without undue delay, on the high seas off the coast of Libya, vessels bound to, or from Libya which they have reasonable grounds to believe are carrying arms or related material to or from Libya."
An arms embargo imposed on Libya in 2011 during the uprising against Moamer Kadhafi remains in force.
International powers have said they would be willing to consider an exemption to the embargo to allow the new government of Prime Minister Fayez al-Sarraj to purchase weapons.
Security Council diplomats however are worried that the weapons shipments could fall into the wrong hands.
The draft resolution calls on the Sarraj government to report to the council about the structure of the security forces and militias under its control and the storage facilities to keep track of the weapons.
British Ambassador Matthew Rycroft said he expected a vote on the draft resolution "in the next week or two."