Grieving family members and the lawyer for hanged man Nguyen Tuong Van have returned to Australia with his body.

Nguyen's mother Kim and twin brother Khoa, along with lawyer Lex Lasry, touched down in Melbourne about 5.30am (AEDT) after travelling on an overnight flight from Singapore.

Mr Lasry addressed the media in the airport's international arrivals terminal as the family side-stepped the waiting media by leaving in a car that collected them from the tarmac.

Nguyen's coffin arrived in Australia as freight in the plane's hold, following his execution by Singaporean authorities on Friday.

The 25-year-old Melbourne man had been on death row after being convicted of importing almost 400 grams of heroin into Singapore in December 2002.

"It's just been a tragic week for all of us, mostly for Kim and Khoa," Mr Lasry told reporters.

He praised Nguyen's courage in the face of death and said the campaign against the death penalty would continue.

There was also sense of relief for Nguyen's family, particularly Kim, Mr Lasry said.

"She is really pleased to be home and - Van was on that flight as well - it's a great relief that this, in a sense, is over," he said.

"She is going to move forward from here, she takes great inspiration and strength from her son.

"So does Van's brother (and) not in the immediate future, but in the longer term, they will get their lives back."

Mr Lasry is calling on the Australian government to formulate a uniform policy on capital punishment in the region.

The Singaporean government had rejected repeated calls for clemency for Nguyen.