"Can you tell me why did you participate in what I think the public has seen as a cover up?" Senator Wong asked deputy secretary in the department of Prime Minister and Cabinet Stephanie Foster.

Ms Foster rejected the accusation, and Liberal Senator Mathias Cormann said the implication of a public service cover up was offensive and wrong.

Mr Morrison has repeatedly refused to confirm a report in the Wall Street Journal that he wanted Hillsong's Brian Houston at the White House dinner, a request that was knocked back in the US.

Public servants appearing at an estimates hearing on Monday confirmed they had prepared an answer to the question, anticipating it would be asked.

The answer cited the need to protect international relations.

It fell to Gerard Martin, a first assistant secretary in the Department of Prime Minister and Cabinet, to face Senator Wong on the subject.

Asked whether the department had provided a list of potential attendees to the United States, he said, "Any matters related to compilation or consideration of the guest list for a state dinner provide by the United States would be a matter that might impact on international relations."

Senator Wong replied, "You've got to be kidding."

Despite interventions from Senator Cormann to head off the line of questioning, Mr Martin eventually answered that the department had not provided a list of suggested names.

Did the Prime Minister's office provide such a list? Senator Wong asked.

To which Mr Martin began to repeat his earlier prepared response, "Any matters related to compilation or consideration ..." before he was interrupted by an irate Senator Wong, who demanded to know who had helped him prepare the set answer.

He responded, Ms Foster.

Asked why she had felt it necessary to help Mr Martin "construct" the answer, Ms Foster said, "We will always prepare ourselves to come to Senate estimates. One of the elements of that preparation is whether there might be information which might, for example, prejudice international relations."

Ms Foster said she wouldn't characterise it as discussing a script.

Senator Wong told Ms Foster she was "disappointed" in the department's approach.

The public had a right to know whether Mr Morrison had asked for Mr Houston's inclusion, and if he had "he should be frankly man enough and brave enough to answer the question".

Senator Cormann said relations with other countries were a legitimate subject for a public interest immunity claim.

Mr Morrison attends a Hillsong-style Pentecostal church, and named Mr Houston as an important figure in his church life in his maiden speech in 2008. Mr Houston has been under fire after the Royal Commission into responses to child sex abuse found that he had failed to alert police to allegations against his father, and had a conflict of interest in the case.

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