The violence erupted in the desert city of Sabha on Friday, the day after the monkey attack.
One hospital official said at least 14 people were dead and 60 people injured in four days of clashes between members of the Gaddadfa and Suleiman tribes.
The United Nations Support Mission in Libya said at least 20 were killed and more than 50 were injured. It and other bodies urged reconciliation.
"My sincere condolences to the victims' families. My thoughts are with them and those injured," said Martin Kobler, Special Representative of the Secretary General and Head of UNSMIL.
"I commend community leaders' efforts to reach a ceasefire and put an end to the senseless killing plaguing Sabha. Voices of reason should prevail, and quickly, for the benefit of the country," he said.
Libya has more than 100 tribes
-- some spreading across the country's borders with Egypt and Tunisia -- but only a few of them hold sway politically. There has been tension between the tribes over the years.
Tribal tension unleashed
The new clashes started after a pet monkey owned by a member of the Gaddadfa tribe attacked a high school girl from the Suleiman tribe on Thursday.
It scratched her face and pulled off her headscarf. Suleiman members retaliated and killed some Gaddadfa men. According to local reports, not yet confirmed by CNN, the monkey was also killed.
Violence persisted afterward. People stayed indoors as gunfire, tank cannons and mortar shells rang out in Sabha early Monday. The city is some 480 miles, or 775 kilometers, south of the nation's capital, Tripoli.
Enmity runs deep between the Gaddadfa and Suleiman tribes, the most powerful armed factions in the region.
Former Libyan leader Moammar Gadhafi, who was ousted from power and assassinated by rebels in 2011
, was a member of the Gaddadfa tribe.
The Suleiman had strongly resented his regime. Shortly after Gadhafi's death, members of the tribe were accused of plotting to overthrow him.
Authorities work to stop violence
Osama Alwafi, a spokesman for the Sabha Medical Center, told CNN the facility has received more than 50 injured people along with 14 bodies. He said the center lacked the resources and the medical staff to handle the emergency.
A member of another tribe who gave his name as Abdusalam and did not want to disclose his full name for security reasons, said that a committee of elder tribesmen from the south met with both parties to try to stop the fighting.
Libya's UN-backed Presidential Council
issued a statement, urging both parties to cease fire while expressing deep regret for the victims.
"The Council calls for an immediate halt to the clashes in the city and urge them to restraint and appeal to reason," the statement said. "The Council has assigned the Interior Minister to open an urgent investigation to determine the causes and circumstances of the clashes and... instructed the Health Minister to follow up the conditions of the injured and the wounded."