The prime minister asked the White House if the pastor could accompany him to the event, but his request was rejected.

"We put forward a number of names, that included Brian (Houston), but not everybody whose name was put forward was invited," Mr Morrison told 2GB radio.

"People have chased this round and round for months.

"At the end of the day what's important is the relationship we have with the United States, and it's never been better."

The prime minister has consistently dismissed speculation about the invitation, saying it was merely "gossip".

Mr Houston was under police investigation at the time over his alleged failure to report his father's sexual abuse of children.

The investigation is still open.

"They're not things I follow closely," Mr Morrison said.

Opposition Leader Anthony Albanese said the prime minister had spent months obfuscating and dodging questions about the invitation.

"For reasons beyond my comprehension, the prime minister said that was just gossip, and now a month later has confirmed that it's a fact," Mr Albanese told ABC radio.

Mr Morrison's office previously refused to release the list of guests he wanted to invite to the dinner, denying freedom of information requests on the basis it would hurt Australia's relationship with the United States.

Australian Associated Press