But concerns have been raised about how money from sports betting will be used to fund national sporting bodies.
The current model sets a minimum of 1 per cent of fixed odds sports betting turnover and 5 per cent of gross betting revenue to be returned to that sport.
In 2017/18, there was $609 million in turnover for fixed odd sports betting, which amounted to $61.9 million in gross revenue after payouts and refunds.
From that, a total of $10.2 million was paid to 34 national sporting organisations.
The bill will see a new model, set in regulation by the Minister of Racing in consultation with the Sports Minister.
The National Party and sporting bodies - including New Zealand Rugby, New Zealand Cricket, Netball New Zealand, New Zealand Football and Tennis New Zealand - have raised concerns that the minister could divert money from the sporting sector to the racing industry, which is estimated to be worth $1.6 billion but has remained stagnant for the past decade.
There have been calls for the sector to have direct involvement in the process of distributing the funds, but Peters rejected that.
"They've got a Minister of Sports and he's being consulted. They can talk to him."
Asked if it was a case of "trust me, I know what I'm doing", Peters said: "Yes it is, and I do."
Sports Minister Grant Robertson has previously said no sporting body would be worse off under changes to the model, and Peters reinforced that today.
"Our objective is to have a far bigger pie and to have them all better off than they are now," Peters said.
He did not know at the moment what the new model would look like.
In a parliamentary select committee this morning, Peters heard from Labour MP Kieran McAnulty, a former bookmaker, who said that the TAB couldn't take bets on mixed martial arts because the sport didn't have a national body.
Peters said the bill would allow sports that do not have an official governing body to apply for a cut of the funding.
He also told the committee that a second tranche of racing reforms, due later this year, could include changes to the $4.8 million tax break for standout yearlings.
Budget 2018 included the funding over four years for tax deductions to be claimed for the costs of high-quality horses acquired with the intention to breed, but by October last year, only two horses had qualified.
Peters said there should be 25 to 30 horses qualifying every year, and how changes to achieve that could be part of the second tranche of reforms.
According to Budget documents, a "standout yearling" is identified by the "virtue of its bloodlines, looks and racing potential".
