BAGHDAD, Iraq (CNN) -- The United Nations estimates that up to 1.6 million Iraqis have left their homes for other countries in "a steady, silent exodus" as a result of the war and sectarian violence, forcing the U.N. refugee agency to announce a shift in priorities. The U.N. High Commissioner for Refugees said it plans to focus on the deteriorating humanitarian situation facing people who are fleeing, as opposed to those returning home. "The enormous scale of the needs, the ongoing violence and the difficulties in reaching the displaced make it a problem that is practically beyond the capacity of humanitarian agencies, including UNHCR," it said. The 2006 budget of $29 million for its Iraq operation was still $9 million short, the agency said, adding that more funding is needed to address the refugee crisis. At least 40,000 Iraqis a month were arriving in Syria, according to U.N. staffers monitoring the border. Refugees have also fled to Iran, and "tens of thousands" are headed to Turkey, Lebanon, Egypt, the Gulf states and Europe," the U.N. High Commissioner for Refugees said. The agency estimated there are half a million Iraqis already in Jordan and 450,000 in Syria, adding that while some have been outside Iraq for a decade or more, arrivals have steadily risen since the war began in 2003.