"He's not going to be given special treatment," Mr Morrison said on ABC television. "He'll get the same treatment and support as everyone else."
Mr Morrison said Mr Assange's matter concerns the US and not Australia.
"It has got nothing to do with us, it is a matter for the US, and there is a range of judicial matters.
"When Australians travel overseas and find themselves in difficulty with the law, they face the judicial systems of those countries."
Labor Senator Penny Wong said it was appropriate that Mr Assange receive consular support.
“There are legal proceedings underway in the UK," she told ABC Radio. "Obviously, there are matters there which will be dealt with by the appropriate legal processes," she said. “As an Australian citizen, he’s entitled to that consular support."
