Hamas spokesman Sami Abu Zuhri on Sunday called the UN mechanism "unacceptable, inefficient."
The UN announced the plan in September, creating a system to bring in badly needed reconstruction materials while sidelining Hamas.
Despite its unhappiness with the system, Abu Zuhri gave no indication that Hamas will disrupt the shipments.
Hamas had remained silent about the plan since UN envoy Robert Serry announced it in September. Serry recently brought in $30 million donated by Qatar to pay thousands of Hamas civil servants who have not received salaries in months.