Libyan doctors have appealed for international help because they are running out of supplies and hospitals are short-staffed.
The NGO Doctors Without Borders says sanctions have put a squeeze on medical equipment getting through.
The capital Tripoli now has just one functioning hospital.
The International Red Cross has delivered emergency supplies to Tripoli and is also sending teams of doctors to help treat the wounded.
It also urged both sides to exercise restraint and allow medical staff to do their jobs.