The chief executive of an embattled construction super fund will appear before a Senate committee on Thursday after being assured he could avoid answering questions about an independent review it had been ordered to undertake about its CFMEU-linked directors.

Cbus Super was under pressure to attend a Senate hearing, chaired by Liberal MP Andrew Bragg, to speak to the nation’s housing crisis and how it could be resolved.

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Chief executive Kristian Fok will now appear before the committee after Bragg in a letter said he could explain to the committee he was unable to answer questions on the prudential regulator’s orders it get an independent review of whether their three CFMEU-linked directors are fit to sit on the board and acted in the best financial interest of members.

Bragg said he would grill Fok on Cbus chair Wayne Swan’s commitment the super fund would invest $5 million in the federal government’s Housing Australia Future Fund, its links to the CFMEU, and the corporate regulator’s Federal Court action against delayed insurance claims.

“The Senate established an inquiry into retirement outcomes, and we’ve been looking at insurance claims handling, housing issues,” Bragg said.

“Cbus has been one of the main funds engaged on these issues. We invited them along with other funds, Housing Australia and APRA [the prudential regulator] and we had real trouble getting them to accept the committee’s invitation.

“After a lot of back and forth I’m pleased they accepted the invitation of the committee. The Senate has very strong summon powers, but that was a last resort I didn’t want to use, and I’m pleased we don’t have to.”

The industry super fund has been under pressure over the past six months after an investigation by this masthead revealed corruption and criminal infiltration in the CFMEU.

That pressure intensified on Tuesday after the corporate regulator revealed it had taken Cbus to the Federal Court for not processing death and disability insurance claims in a timely manner.