According to a statement published by the ICRC on Monday, fighting near the Iraqi border has forced hundreds of women, children and elderly persons to flee their homes and take refuge in surrounding areas.
The press release also urged "all those involved in the fighting to respect the basic rules of international humanitarian law" and called for an end to attacks on civilians, the poor treatment of wounded fighters and an end to discrimination in caring for the sick.
"The ICRC calls upon all those involved in the fighting to take every feasible precaution to spare civilians and to ensure that the principles of distinction and proportionality are respected in all military operations."
The ICRC's statement was made a few days after the US military ended a major offensive which began on 7 May to root out what its military commanders said were followers of Jordanian-born Abu Musab Zarqawi.
The fighting in al-Qaim has
displaced thousands of civilians
The US army says the remote desert region is a haven for foreign fighters who slip across the border along ancient smuggling routes.
But fighters in al-Qaim, 320km west of Baghdad, insist there are no foreigners among them.
Thousands of people fled al-Qaim after US warplanes and helicopter gunships pounded the region earlier this week, flattening homes and other buildings.
Al-Qaim's hospital was damaged in the shelling and doctors tended to bloodied young men at a makeshift facility set up in a private home over the weekend.
The victims said a rocket slammed into them as they were standing on a bridge over the Euphrates river, killing two of them and wounding six.
On Friday, US fighter jets destroyed a suspected safe house used by the fighters in Karabila village, after marines took fire from at least four fighters in the building, the US military said.
The US military has confirmed 10 marine deaths so far and says about 125 fighters were killed in the operation.
Despite the instability, humanitarian organisations say they are continuing their relief work in the region.
In Akachat, located in an isolated desert area near al-Qaim, the ICRC is providing 135,000 litres of fresh water per day to hundreds of displaced families.
The Iraqi Red Crescent Society also began trucking in aid to al-Qaim from 13 May. Food and non-food items have been distributed to roughly 200 families in Rawa, 250 families in Ana and 500 families in Akachat.