Wayne Swan, a former federal Labor treasurer, blamed the issue, which affected more than 10,000 insurance claims, on an offshore third-party operator tasked with processing the payouts.
"But we are ultimately responsible for that, and we accept that responsibility," he told Nine's Today show on Friday.
"We're sorry it happened and we're determined to ensure it never happens again."
Mr Swan added, "I do accept complete responsibility for it".
At a Senate hearing in Canberra on Thursday, Cbus chief executive Kristian Fok said the fund had resolved more than 6000 claims.
Those members and their beneficiaries had so far received $755 million in benefits, he added.
Cbus chief executive Kristian Fok apologised at a Senate hearing in Canberra on Thursday. (Lukas Coch/AAP PHOTOS)
"I do want to again say sorry for the impact that the delays in processing of insurance claims have had on our members and their families," he told the hearing.
"Many of our members hold high-risk jobs where injuries and death are more common.
"We know that delays in processing claims can add to their distress at a difficult time."
Mr Swan confirmed those affected would also receive compensation.
The Australian Securities and Investments Commission on Tuesday announced it was taking Cbus to the Federal Court over allegations it failed to pay more than 10,000 claims in less than 90 days.
It also alleged more than 6000 claims had been delayed more than 12 months by late 2022 - more than half the fund's claims at that time.
The corporate regulator is seeking penalties, adverse publicity orders and compliance matter orders through court.
Cbus, which is linked with unions including the CFMEU, manages $94 billion in assets, according to its website.
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