At least 2,200 people have fled from fighting south of the Libyan capital Tripoli, the United Nations humanitarian office has said in a report.
It added that many civilians were trapped and cut off from emergency services.
"The fast increasing deployment of forces could potentially result in significant population displacement," the report said.
It said aid agencies on the ground had enough emergency medical supplies and trauma kits to treat up to 210,000 individuals and 900 injuries for three months.
At least 32 people have been killed and around 50 wounded in fighting with Khalifa Haftar's troops near Tripoli, the UN-backed government said.
The health minister gave the updated death toll in an interview with Libya's Al-Ahrar television station late last night.
Mr Haftar's forces have so far said 14 of their fighters have died.
Fierce clashes raged yesterday near Tripoli between pro-Haftar fighters and troops loyal to the internationally recognised Government of National Accord (GNA).
The two sides also exchanged air strikes days after Mr Haftar, who backs an administration in eastern Libya opposed to the GNA, launched an offensive on Thursday to seize the capital.
The clashes came despite calls by the United Nations and the United States for an urgent ceasefire.
Pro-GNA forces yesterday announced a counteroffensive named "Volcano of Anger".
A spokesman said the operation was aimed at "purging all Libyan cities of aggressor and illegitimate forces", in reference to Mr Haftar's fighters.
Libya has been riven by divisions since the NATO-backed uprising in 2011 that killed dictator Muammar Gaddafi, with rival administrations and armed groups vying for power and control of the country's oil.
Mr Haftar's offensive has threatened to plunge the country into a full-blown civil war and once again thwart diplomatic efforts to find a solution to Libya's woes.