The fighting, which left nine dead and more than 50 wounded, had prompted many to flee their homes and forced schools and shops in and around the camp to close.
The commander, who spoke on condition of anonymity, said the local security force, which includes 100 fighters from several Palestinian factions, was able to deploy throughout the camp after a ceasefire late Wednesday night.
Lebanon's army does not enter the camp by long-standing convention.
He added that "extremist Islamist groups" had withdrawn from some areas to avoid further clashes.
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Fighting erupted late Friday after Palestinian factions deployed throughout Ain al-Hilweh as part of an operation aimed at combating the influence of a local Islamist group linked to Bilal Badr, a wanted militant.
The commander said Badr had refused to give himself up to Palestinian security forces to be handed over to the Lebanese authorities.
Badr is wanted on suspicion of "terrorism", firearms offences and belonging to an armed group, according to a Lebanese security official.
Local activist Asef Moussa told AFP that "dozens of young people will volunteer on Friday to clean the streets and clear up the damage and rubble left by the fighting".
The United Nations Palestinian refugee agency UNRWA said it welcomed the return to calm.
"UNRWA... Is working to restore its services in the camp as quickly as possible," said its local affairs director Claudio Cordone, adding that UNRWA would resume its activities on Friday morning.
Ain al-Hilweh is the most densely populated Palestinian camp in Lebanon.
Lebanese security forces do not enter Palestinian refugee camps, where security is managed by joint committees of Palestinian factions.