Maurer arrived Monday in Iraq for a four-day visit with political and religious leaders. Upon his arrival, he said ongoing violence in the western province of Anbar was taking its toll on civilians.
"We urge everyone involved in fighting to spare civilians and allow humanitarian and medical personnel to carry out their duties in safety," he said in a statement.
Iraqi Prime Minister Nouri al-Maliki, a Shiite, is struggling to stabilize a country witnessing a rise in al-Qaida activity, particularly in western Anbar province. U.S. officials have said al-Qaida is exploiting political divisions between Shiite and Sunni leaders in the country.
Maurer said the ICRC has provided assistance to more than 52,000 people displaced from Anbar since conflict erupted in late 2013.
Last week, Adrian Edwards, a spokesman for the U.N. High Commissioner for Refugees, said parts of Fallujah, the provincial capital, are under siege.
A government cease-fire ended last week and the UNHCR says violence has since erupted on the outskirts of the city.
U.S. forces twice battled Fallujah insurgents before ending combat operations in 2011.