The first headsets were due to have arrived with customers on 28 March, but many are still waiting.
The firm has blamed an “unexpected component shortage” and says customers should receive updated news on their orders by 12 April.
Oculus founder Palmer Luckey said he had no further information to share.
Mr Luckey was responding to a thread on Reddit, the world’s largest community forum, which appealed directly to him.
“Don’t shunt blame to other people, this is my call,” he wrote.
“I am not going to wax poetic about this, since I have done so in the past, but bottom-line: I won’t give in-depth updates on any situation without knowing it is solid, true, and finalised.
“Until I can do so, the best I can do is remind people that I will get them information as quickly as I can.”
Mr Luckey personally delivered the first Rift headset to a customer in Alaska last week. He posted a video of the handover on Facebook.