The eastern Libyan National Army force (LNA) forces loyal to Khalifa Haftar confirmed a strike late on Sunday on the town, but denied they had targeted any civilians.
The Tripoli-based internationally recognized government opposing Haftar said dozens were killed and wounded.
Reached by telephone, Murzuq municipal council member Mohamed Omar told Reuters: "The air strike resulted in 43 killed and 51 wounded. This is only an initial toll of casualties."
The LNA had at the start of the year taken Murzuq as part of an offensive to control the oil-producing south. But it later moved out to concentrate forces north where it has been trying to take the capital Tripoli in a four-month campaign.
The LNA said in a statement its strike had targeted "Chadian opposition fighters," a phrase that usually refers to Tebu tribesmen opposing them in the area.