The U.S. military has said that an American service member has been killed while conducting military operations in northern Iraq. The military statement released Friday said the death occurred Thursday. It gave no further details of the incident. Violence has dropped dramatically across Iraq, but deadly bombings and shootings still happen nearly every day. Some officials have warned of an increase in attacks as the U.S. withdraws all of its 33,000 troops from Iraq by the end of the year. The incident is under investigation, the statement said. The name of the deceased is being withheld pending notification of next of kin. The death raises to at least 4,484 the number of U.S. military personnel who have died in Iraq since the war began in March 2003.