In an interview in The Australian newspaper, Mr Bush said Australia and the US were equal partners, friends and allies.
Asked whether he saw Australia as the US's deputy sheriff in South-East Asia, Mr Bush said: 'No. We don't see it as a deputy sheriff. We see it as a sheriff. There's a difference.'
Speaking to reporters about a $3.5 billion submarines contract, Senator Hill was reluctant to be drawn on the president's comments.
'It's not my language,' he said.
'I'm not interested in the sheriff comments.
'I'm not sure what it means.'
Senator Hill said he thought the US-Australian alliance was in very good shape.
Why, God, why?