Sunni leaders have said Iraqi Prime Minister Nouri al-Maliki, a Shiite, is marginalizing members of their society. U.S. officials have said terrorists in Iraq are now exploiting those divisions and al-Qaida this year has taken over parts of Anbar, a mostly Sunni province.
The ICRC said at least 26,000 people have been displaced by violence in Anbar since the beginning of the year.
"The consequences for civilians of the escalating violence in the Iraqi province of Anbar are growing as fighting shows no signs of letting up," the agency said in a statement.
Maliki wrote in the U.S. news magazine Foreign Policy this week the threat from terrorism in his country was "transnational in nature, and defeating it will require international cooperation."
U.S. military forces twice battled terrorist groups in Anbar before ending combat operations in 2008.
Maliki said security operations in Anbar "may take time" but denied the conflict was part of a sectarian divide in Iraq.
Maliki is competing for a third term in office during April elections.