Under the bill, a written agreement would be required to clarify the terms of layby sales.
It includes a clause that would mean sellers would bear the responsibility for ensuring a product was kept in good condition before the buyer took it home.
Mr Tremain said many people presumed they were protected, but that was not the case.
The new law would also spell out clearer rules around cancellation of sales, allowing a buyer to back out of a layby purchase at any time before paying off the product.
The seller could not charge a cancellation fee unless it was in the agreement.
On Trade Me, "a consumer has the same rights under the Consumer Guarantees Act to have their goods replaced, to expect fair quality," Mr Tremain said.
He added they were "all the standard provisions that a consumer could expect if they were walking into a store and buying something off the shelf."
The law would not apply to one-off and casual traders on the website.
In addition, the bill would give the Commerce Commission a wider range of tools to enforce the Fair Trading Act, and amend the Consumer Guarantees Act to better provide for acceptable quality of electricity and gas.
It would also provide for a new Auctioneers Act to require auctioneers to meet minimum standards.
"The consumer legislation really hasn't been updated in 20 years," Mr Tremain said, "so it strengthens consumers' rights and helps simplify compliance so everyone knows exactly where they stand."
As well as online auctions, the bill also covered other consumer technology, including self-service supermarket tills.
NEW SHOPPING LAWS
* Mandatory formal agreements for laybys.
* Ensuring the seller keeps the goods in good condition.
* Cancellation rights without penalty.
* Bring Trade Me sellers into the realm of the Consumer Guarantees Act.
* More powers to enforce the Fair Trading Act.