Ansar al-Sharia is already on the US terror list for its role in the September 2012 attack on the US mission in Benghazi that killed the US ambassador and three other Americans.
A copy of the French-led request to the Al-Qaeda sanctions committee was obtained by AFP.
Inclusion on the UN terror list means members of the group are subject to visa bans, asset freezes and an arms embargo, and the move more broadly cuts the group off from the political mainstream.
French Foreign Minister Laurent Fabius in September told a meeting on the sidelines of the UN General Assembly that the group should face sanctions as part of efforts to prevent Libya from sliding further into violence.
In the request to the Security Council, the three countries asked that Ansar al-Sharia Benghazi and Ansar al-Sharia Derna be blacklisted, arguing that both groups have ties to Al-Qaeda in the Islamic Maghreb (AQIM) and other extremist groups.
Since 2012, the Benghazi wing has operated several terrorist training camps mainly to help armed groups in Iraq and Syria and to a lesser extent in Mali, according to the request.
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Twelve of the 24 jihadists who attacked the Algerian In Amenas gas complex in 2013 trained in the camps of Ansar al-Sharia in Benghazi, Libya's second city, the documents said.
More recently, the group has conducted several attacks on Libyan security forces, it added.
Ansar al-Sharia Derna also took part in the 2012 attack on the US mission and is operating camps in the northeastern Derna and Jebel Akhdar regions to train fighters for Iraq and Syria.
This month, Ansar al-Sharia Derna pledged allegiance to ISIL, the Islamist group that has seized control of territory in Iraq and Syria, according to the documents.
The Security Council has until November 19 to raise objections to the proposal.
On Monday, Libyan pro-government forces launched an attack on districts held by the Islamist militias around Benghazi.
Libyan authorities have struggled to assert control across a country awash with weapons and powerful militias which ousted longtime dictator Moamer Kadhafi in a 2011 revolt.