There was none of the enthusiasm that marked Libya's first free election in July 2012 as public frustration mounts over the weak central government's failure to restore order in the wake of the Arab Spring uprising.
In the first four hours, turnout had reached just 18 percent, election organisers said.
"I am on the electoral register but I am not going to vote, just because I don't know who to vote for," said Amal, a 21-year-old travel agent.
A threat by powerful former rebel militias to dissolve the interim General National Congress (GNC) elected in the 2012 poll had meanwhile ramped up pressure on the weak central government ahead of the vote.
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"All of us are aware that in a transition, a second election may not motivate people and mobilise energies in the same way the first elections did," he said.
Khairi Chokwara, 52, said he could not understand his compatriots' lack of interest in going to the polls, as he proudly showed off the indelible ink on his finger that showed he had voted.
"For me, these elections are the most important ones because it's through the new constitution that we will chart our country's future."
The interior ministry said it deployed more than 40,000 police to secure the North African nation's 1,500 polling stations, while the defence ministry said it posted 11,000 troops.
Despite the security measures, gunmen killed the caretaker of a school in the eastern city of Derna that was to be used as a polling station, local NGO coordinator Abdelbasset Abu Dhahab told AFP.