On Saturday, the U.N. Support Mission in Libya expressed concern about civilian casualties in the town of Bani Walid, near Misurata.
Tarek Mitri, U.N. special envoy to Libya, said a mediated settlement to the conflict is "urgently needed."
The fighting came on the first anniversary of the death of Libyan leader Moammar Gadhafi, who died after falling into rebel hands. The New York Times said at least 22 people were killed in fighting between area militias and rebel fighters near Bani Walid, a former Gadhafi stronghold.
Area militias have reportedly fired on civilian areas and the Times reported Bani Walid residents marched on Parliament last weekend calling for an end to the violence.
Ishfaq Muhammad Khan, head of the International Committee of the Red Cross delegation in Tripoli issued a plea for calm.
"We're very concerned," he said in a statement. "We urge all parties to act with caution, to respect human life and to spare medical personnel and facilities at all times."
The ICRC said it made repeated visits to deliver medical supplies to Bani Walid during the past week.
Notable deaths of 2014 [PHOTOS]