But National Party sport and recreation spokeswoman Nikki Kaye said the bill provided no funding certainty for sporting organisations.
"In my view, there is a real case to look at whether all proceeds generated by a sport should be allocated back to that sport," Kaye said.
"We are talking about significant core funding for organisations such as Netball New Zealand, NZ Rugby, NZ Cricket and NZ Football."
NZ Cricket spokesman Richard Boock agreed with Kaye's concerns, saying her comments were "fair and representative of our position".
"And they reflect concerns that we've been making for some time."
But a spokeswoman for Robertson gave assurances that sporting bodies would not be worse off.
"Sport will not lose out from these changes."
The spokeswoman said the allocation of charges to racing and sport would be set out in regulations, and the regulatory framework was still to be determined.
"Having Sport NZ distribute funds to sports makes sense as they are well positioned to understand where the areas of greatest impact and need are within the recreation and sport system."
NZ Rugby chief executive Steve Tew said that any reforms should improve commission payments to national sporting organisations to "fairly reflect the contribution our content makes to New Zealand's betting sector".
"Ideally, we would also like to see NZ Rugby and other sports having more of a voice within the governance of this industry. It remains unclear as to whether this bill will achieve those objectives."
Kaye said National supported the bill's first reading because it wanted to ensure the viability of the racing industry, but more time should have been allocated for public submissions.
"Why are we taking a short couple of weeks on a bill that may impact thousands and thousands of kids who play sport, because of the impact to the national sporting codes?" Kaye said during the first reading.
Transparency International NZ also criticised the process, calling for an extension in the interests of transparency and public trust.
"There is a reasonable public expectation of full and thorough opportunities for public involvement in matters of public debate such as gambling," Transparency International NZ said in a statement.
Peters is overseas and unavailable for comment, but he justified the select committee process when he spoke during the bill's first reading last week.
"A shortened select committee period is requested to allow Rita [the Racing Industry Transition Agency] to start work immediately on transitional arrangements."
He said a second bill to reform the industry would proceed later this year and include a fuller select committee process.
Peters added that the new funding model, including an information-use charge and a point-of-consumption charge for offshore bets, would make the system fairer.
"Currently, unlike the New Zealand-based provider, overseas betting operators aren't required to contribute to the cost involved in conducting racing and sports in New Zealand.
"These offshore charges will ensure that overseas betting operators start to contribute to New Zealand, including to the racing and sports codes from which they benefit."
