"We want to ensure that internet broadcasters know what standards apply to election-related materials online, and that the public know who to approach with relevant related complaints," the letter said.
Live-streaming has been complicated because it exists somewhere between broadcasting and on-demand content.
The Broadcasting Act provides a specific exclusion for on-demand content in that it involves pre-recorded content that's accessed for personal viewing.
The BSA argues that live-streaming is different to this, comparing it to "switching on a television and selecting the channel".
The point the BSA makes is that live-streaming isn't a private transmission for one person alone, but is rather transmitted "to all linear, live-stream or simulcast viewers".
Should live-streaming fall under the Broadcasting Act, it will have major implications for companies such as Facebook and YouTube.
The Broadcasting Act provides rules specifying what kind of content is allowed to be broadcast in New Zealand This includes rules related to good taste and decency, children's interests, violent content, accuracy and privacy.
Under the Act, broadcasters are required to ensure that broadcasts on their platforms always comply with these standards.
They are also required to have a proper process for dealing with complaints and should refer any complaints to the BSA if complainants are not satisfied with the response to their original complaint.
The BSA says it will work with broadcasters to prepare an internet broadcasting code that will contain guidelines applicable to online broadcasting. This will add to the already-existing radio, free-to-air television and pay television codes.
The BSA plans to start working on this code in January next year but has stressed the importance of acting quickly to ensure rules are evolved to be suitable for technologies that exist now and may develop in the future.
The BSA is calling on media owners to submit their feedback on the rules by 13 December and hopes to reach an agreement on how the law is applied.
In the event that consensus is not reached, the BSA is willing to take the legal route to establish the framework.
"If legislative interpretations issues prove too much of a barrier, we will consider seeking a declaratory judgment on notice to those who wish to participate in the process to clarify any issues we cannot agree upon," the letter says.
The issue of live-streaming has proven particularly contentious in New Zealand in the wake of the Christchurch terrorist attack.
Although the original video was only viewed 200 times while live, it quickly spawned over a million videos containing footage of the bloodshed.
In the aftermath of that, Facebook incorporated a one-strike policy, which temporarily restricts access for users that break the social media site's rules.
A Facebook spokeswoman told the Herald the company is currently reviewing the changes proposed by the BSA.
"We've called for governments and regulators to create rules for the internet to help protect society from broader harms while also preserving the freedom of people to express themselves," she said.
"People use dozens of content sharing services every day and it's important for governments, industry and civil society to work together to on smart, standardised rules for online content.
"The New Zealand Government's already leading on this important work, which is why we've hosted workshops with them on how we build products, engineer artificial intelligence and enforce our Community Standards. We welcome the opportunity to work with all parts of the New Zealand government on smart regulation for the internet."
Google declined to comment for this article.