A spokesman for Mr Morrison toldThe Age andThe Sydney Morning Heraldthe guest list was a matter for the hosts.
“Invitations to the state dinner are entirely at the discretion of the White House as has been the case previously,” he said.
Mr Houston rejected the story on Saturday,saying he"had no invitation to the White House"and had not discussed it with Mr Morrison or anyone else.
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"Hillsong Church received no enquiry from any party as to my details or availability. As far as I’m concerned this is baseless rumour and totally false news,"he said in a statement.
The founder of the multimillion-dollar Hillsong mega-church has a long-standing relationship with Mr Morrison,who is a member of another church in Australia's Pentecostal Christian movement.
In his first speech to Parliament,Mr Morrison said he had been"greatly assisted by the pastoral work of many dedicated church leaders"and specifically thanked Mr Houston.