Andrew Bowater, Huawei NZ's deputy chief executive, told delegates Huawei had a 14-year history in New Zealand, and had opened itself up to "unprecedented" scrutiny via the UK's intelligence and security network GCHQ.
He called on the minister to talk to the company - something Little has so far refused to do.
Bowater's speech is part of a strong public relations push by Huawei to regain public trust and get its network technology back into the 5G rollout, after being banned by the Government Communications Security Bureau last year.
The campaign includes its quirky "5G without Huawei is like rugby without New Zealand" advertising campaign and an opinion piece on Stuff this morning headlined "We know the rumours, gossip and innuendo about us."
Bowater said at the China summit "GCHQ has said it has never found any evidence of wrongdoing from Huawei. Not one of our competitors has opened themselves up to that sort of scrutiny, nor has it been asked for."
Its main competitors are Finnish company Nokia and Swedish multinational Ericsson.
Bowater said Huawei had approached Little for a meeting, but had been told that was "inappropriate", while the 5G process was going on.
"We think it's appropriate to have a broader engagement."
Bowater said the GCSB decision was more about geopolitics and was not the best outcome for New Zealand in terms of its technology.
"We are confident we could mitigate any risks."
He quoted UK estimates of a £6 billion impact on the economy there if the government banned Huawei and went for a duopoly vendor situation.
Similarly, the impact in New Zealand could be "huge" - potentially hundreds of millions, he said.
Last month, the UK government formalised a ban on Huawei's involvement in the core 5G network there but left open its ability to participate in the rest of the build.
Huawei argues that the part of a 5G network at risk from any potential Chinese government interference is the core, which will be supplied by US company Cisco.
Huawei is only bidding to put its technology on the 5G cellsites, which are one step removed from the core.
"We don't play in the core - that's the brains and where the data is managed, and that's where New Zealand might get attacked," Bowater said.
The GCSB told Spark that using Huawei 5G equipment would, if implemented, raise significant national security risks.
Bowater said Huawei would like the opportunity to put its case directly to the government.
"We believe after 14 years in the market, we deserve the right to a fair trial."
GCSB director general Andrew Hampton said it assesses proposals from network operators to identify potential significant risk, using a framework that's agnostic of suppliers and the country of origin for the equipment.
"While I cannot comment on particular notifications as these are made to us on an in confidence basis, I am aware of ongoing commentary on the use of Huawei equipment in 5G networks," he said in a statement.
Because of the nature of 5G networks - which consist of densely-packed small cell sites rather than large spread-out antennae - it's harder to isolate sensitive aspects of the network, he said.
"GCSB uses information, including classified intelligence, from a wide range of sources in making our assessment of network security risk. While we have access to information from Five Eyes partners, and other sources, the decisions we make are independent, in accordance with New Zealand law, and based on our own assessment," he said.