"The ICRC is deeply concerned about the growing violence in various parts of Iraq, such as Kut, Baghdad (Sadr City), Samara, Falluja and Najaf," the organisation said in a statement on Thursday.
On the eighth day of fierce battles in the city of Najaf, the Red Cross called on both sides to ensure civilian lives are spared and that the sick and wounded are quickly evacuated.
"Fighting in these heavily populated areas are increasing the risks of civilian casualties and hampering basic services," it warned.
The Geneva-based agency it had provided three tonnes of emergency medical and surgical aid in a bid to relieve war-ravaged civilians in Najaf - the scene of some of the heaviest fighting between US occupation forces and the Al-Mahdi Army loyal to cleric Muqtada al-Sadr.
In cooperation with the Baghdad health department, the ICRC has delivered sufficient aid - including anaesthetics, painkillers, IV fluid and antibiotics - to help 200 patients, and said it was ready to provide more if necessary.
Nationwide fighting in the past 24 hours has left some 165
Iraqis dead and 600 wounded.