Afterwards, Ms Jagose said the interruption was very disappointing.
"Protests are a legitimate part of the democracy that we live in, and I like the democracy that we live in. So is the work that the bureau does - a legitimate part of the democracy that we live in, so it is a shame that one stopped the other from going ahead today."
Ms Jagose said she would have spoken about the work the GCSB does in foreign intelligence and cyber defence, and the systems of oversight that are in place.
"I was going to talk a lot more than we have ever talked about before in public about our cybersecurity programme, called the Cortex programme - how we look at the privacy interests related to that programme, how it works, how it is controlled, what it is. Stuff that we have never said before.
"We will look for an opportunity to get that out. Because I think the public want to know. We need to take a breath and find a way to do that, because it is a story that needs to be heard in its entirety."
Cortex is a cyber-shield that is designed to protect government agencies and other organisations, such as power companies, from cyber attacks.
Its existence was first revealed by Prime Minister John Key before last year's election, and ahead of Kim Dotcom's "moment of truth" event in Auckland.
"What I was going to show is what that is, why it is entirely proportionate to the threats that we see in the cyber world, and why what we are doing is about protecting New Zealanders and New Zealand's interests," Ms Jagose said.
The GCSB is responsible for keeping sensitive government data secure and also provides protection to selected private companies through a cybersecurity programme.
It has reported advanced attacks as becoming more common.
Asked if serious incidents were becoming more common, Ms Jagose said statistics would be released shortly.
"The threat about cyber is the connectedness to the internet, so as that increases, as it does almost every day, yes the threat increases."
Mr Edwards, whose office organised the event, said he did not ask security to remove the protesters as he did not want to subject Ms Jagose or the audience to such a spectacle.
"That would have suited the protesters I am sure...but there is no need for that. This is about freedom of speech. They have their speech, and if they use it to shut down this really important development and opening up of the organisation, then I think they have acted counter to their interests, frankly."
Mr Edwards said his role was keen to host such events and by doing so give some assurance to the public about the activities of the country's intelligence agencies.
"You had those protesters asking why is the Privacy Commissioner doing this? And they are not even listening to the answers.
"I am not going to have a process of vetting, and I'm not going to have a security to drag people out. If people want to come here to have a respectful conversation, they are welcome. If they are not, then maybe we question whether we can.
"But I would be really disappointed if we were forced to not proceed with events that actually illuminate really important matters of privacy at a critical time for public trust and confidence."
One of the two protesters, well-known Wellington activist Valerie Morse, said she believed such events were a propaganda exercise.
"Five Eyes has been implicated in drone strikes...we are really concerned that the Privacy Commissioner thinks it's an appropriate thing to conduct these discussions with the most secretive spy agency."
Ms Jagose's scheduled talk reflects increased public relations efforts by the agency, and comes after Rebecca Kitteridge, director of the Security Intelligence Service (SIS), addressed a privacy and identity conference in May.
Both the domestic intelligence agency the SIS and GCSB, with its foreign intelligence mandate, have come under intense scrutiny after a series of revelations and allegations.
Cheryl Gwyn, who as the Inspector General of Security and Intelligence and Security is responsible for independent oversight of both agencies, has started inquiries into the activities of the GCSB.
They are linked to claims the agency spied on foreign diplomats competing against Trade Minister Tim Groser to lead the World Trade Organisation, and allegations it conducts surveillance on Pacific nations, including New Zealanders living and working in the Pacific.
A wide-ranging review of both the SIS and GCSB, headed by former Deputy Prime Minister Sir Michael Cullen and lawyer Dame Patsy Reddy, is expected to report back by February next year.
