Envoy Bernardino Leon, who has been shepherding peace talks between Libya's rival parliaments, presented what the UN mission (UNSMIL) described as the "basis from which the parties can work" towards a solution.
The proposal was delivered at meetings in Tripoli and Tobruk, where the rival parliaments are based.
In the latest violence, a suicide car bombing in the country's second city Benghazi killed seven soldiers today, military sources said.
It "cannot afford to wait any longer before there is a settlement that could restore security and stability and end the suffering of the people".
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Samir Ghattas, a spokesman for UNSMIL, told AFP by email: "The visit to Tobruk was good. The objective was to pass on the message to the speaker and that was fulfilled.
"There was a long conversation with the foreign minister, (Mohamed) al-Dayri, at the airport who has been in contact with the House of Representatives, and they sent a positive message."
A national security council and a municipalities council would also be created. An existing constitutional drafting committee will also be part of the transitional period.
All will operate for a "transitional period whose duration will be agreed on by the parties and will end with new elections that will come after the approval of the constitution and referendum," UNSMIL said.
The mission noted that the proposals are "first and foremost Libyan and formulated after wide discussions" that address the concerns of all sides and call on the sides to "make concessions".