But the Government is increasing the pressure on Mr Shorten over his time as head of the Australian Workers Union and membership-stacking claims.
The Government says it's what Mr Shorten knew about deals under investigation by the Trade Union Royal Commission that he needs to explain.
Labor leader Bill Shorten is coming under strong pressure to explain what he knew about annual invoices to a construction company for union memberships.
The unions royal commission has been told it happened in 2005, when he was in charge of the Australian Workers Union.
The Victorian branch of Mr Shorten's Australian Workers Union allegedly invoiced a construction company for over $38,000 to pay for 105 union memberships.
The commission has also heard the same union enrolled an entire Victorian basketball team which knew nothing of the deal until an invoice arrived in the mail.
Mr Shorten says the agreement with the company Winslow Constructors was registered in the industrial commission and delivered pay rises to workers.
But acting employment minister Christopher Pyne says the public deserves to know why the money was given to the union.
"Now this is becoming an open sore for Bill Shorten. He needs to address it. He needs to apply the balm of sunlight to exactly what he knew and when about the arrangements with Winslow Constructions. And until he does, he'll continue to be dogged by this particular issue."
Labor frontbencher Anthony Albanese has defended Mr Shorten.
He argues Mr Shorten was committed to advancing workers' living standards and is willing to cooperate with the royal commission.
Mr Albanese has told Channel Nine the inquiry should be able to run its full length separate from political commentary.
"The royal commission needs to be able to do its job and do it separate from political engagement and commentary on a day-by-day basis. It will do that. Bill's made it very clear he'll cooperate with any inquiries that the royal commission wants to take. But this is a legal process. Legal processes need to be separate from political processes."
The man who succeeded Mr Shorten as Victorian AWU secretary, Cesar Melhem, has been stood aside as a whip in the Victorian parliament.
He is fighting allegations being aired in the royal commission in relation to Winslow and other companies.
Mr Shorten says he has zero tolerance for corruption or illegality in the workplace.
He has insisted any deals he approved at the helm of the AWU always led to better pay and conditions for his members.
And he has sought to deflect the issue by trying to reframe the debate to focus on the need for constitutional change to make Australia a better place.
He says, if Australians had their say now, the first sentence of the constitution would recognise Indigenous people.
And he says the country should not have to wait until the Queen dies to start talking about an Australian republic.
"I believe there are two major priorities for constitutional change in this country. One, recognising Aboriginal and Torres Strait Islander people as the traditional owners of our continent. And two, an Australian republic with an Australian head of state. Now these are two very different challenges. And there are different lessons from 1988 and, indeed, 1999 that we can apply to each of them."
Mr Shorten and Prime Minister Tony Abbott are due to meet Indigenous leaders on July the 6th to consider the model for a referendum on Indigenous recognition.
The co-chair of Reconciliation Australia, Tom Calma, says he hopes a July referendum summit in Sydney will produce some changes towards constitutional recognition.
Mr Calma says he hopes the meeting will finally give some clarity on the way forward.
"If it's really just an open sheet, then it could go anywhere. So, whilst there needs to be some parameters around what's discussed, I think it also needs to be structured to allow people to express their views fairly openly."
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