The U.N. says the services at Camp Hurriya are already far better than at most other refugee camps worldwide.
On Tuesday, Iraqi National Security Adviser Faleh al-Fayadh warned the group to move soon or his government will take matters into its own hands.
Ban urged the refugees to "earnestly prepare for their next transfer." He added that "violence should, at all costs, be avoided" and urged Iraq's government to "exercise restraint."
Shahin Gobadi, a Paris-based spokesman for the group, said in an email that the infrastructure is inadequate and nobody will move there until it is improved. He said the People's Mujahedeen Organization of Iran had offered to pay for improvements and to cover the cost of the next convoy.