Australia's Christian Prime Minister Scott Morrison has said it is "entirely appropriate" that Brian Houston has stepped down from Hillsong over alleged inappropriate behaviour.

Houston co-founded Hillsong nearly 40 years ago and resigned earlier this week as its Senior Global Pastor.

In a statement, the board said he had breached the Pastor's Code of Conduct.

Morrison has been criticised over his connections to Hillsong.

In his 2008 maiden speech, Morrison credited Houston with helping to shape his Christian faith, and in 2019, he addressed the annual Hillsong conference from the stage. 

Morrison shared his reaction to Houston's resignation with reporters on Thursday. 

"I must admit we were very disappointed and shocked to hear the news," Morrison said.

"My first thoughts were with the victims, as they've been rightly described and so I was very concerned.

"And the actions that have been taken are entirely appropriate."

Hillsong announced Houston's resignation on Wednesday. In a statement, it said Houston had been investigated over allegedly sending "inappropriate" text messages to a Hillsong staffer, and a separate complaint that he had entered the hotel room of a woman who was not his wife. 

"As you can appreciate, there is still much to be done and our church leadership continues seeking God for His wisdom as we set the course for the future. We acknowledge that change is needed," the board said. 

Phil Dooley is acting senior global pastor of Hillsong in place of Houston.