Syria had said last month that work on the destruction of the 12 hangars and tunnels would begin in November, but the Syrian company chosen to conduct the operation pulled out.
Two other Syrian companies were picked but the firm tasked with destroying five tunnels is waiting for deliveries of explosives and equipment, said Syria's UN Ambassador Bashar Jaafari.
"The Syrian government emphasizes that any delay in the delivery is the responsibility of the international parties, and not that of the Syrian government," he told reporters at UN headquarters.
"The destruction process of the 12 empty production facilities... is scheduled to begin later this month with the destruction of the first tunnel," he said.
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Jaafari said it should be completed by June.
The UN Security Council heard a final report from special envoy Sigrid Kaag, who leads a UN mission to rid Syria of its chemical weapons in line with an agreement reached by Russia and United States.
Chadian Ambassador Cherif Mahamat Zene said the 15 members of the council had expressed their "concern about the need to destroy the 12 remaining production sites and to respect the timetable for the destruction."
A total of 1,300 metric tons of chemical weapons have been removed from Syria and most of those were destroyed on board the US Navy ship MV Cape Ray.
After an August 2013 sarin attack outside Damascus that much of the international community blamed on President Bashar al-Assad's government, the regime agreed to turn over its chemical arsenal.