The six students, all aged 21 and 22, died early Tuesday when a fourth-floor apartment balcony collapsed during a birthday party at the complex in Berkeley, two blocks from the University of California campus.
The parents of the five Irish students killed in the accident thanked the community for its support and applauded the victims' friends for the response after the balcony crashed to the ground.
"We cannot thank enough the students that were in the apartment and apartment complex that night. The manner and speed at which they reached out to our families, to our Consul, and to each other was faultless," the statement added.
"Our children were extraordinarily blessed in their friends and we are enormously proud of them."
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The five Irish citizens were to be sent back to Ireland yesterday, the statement said, while an Irish-American student was buried in Sonoma, California earlier in the day.
"We now ask for privacy so that we can mourn the sudden and tragic passing of our beloved sons and daughters, with the dignity that they deserve."
But they said they were grateful for the outpouring of support, and said it was a "testament to their popularity, and to the closeness of these groups from school and university."
At least seven people were injured in the accident, with some in critical condition.
The victims were identified as 22-year-old Ashley Donohoe, an Irish-US dual citizen from California; and Olivia Burke, Eoghan Culligan, Niccolai Schuster, Lorcan Miller and Eimear Walsh, who were 21 and from Ireland.