In its first comment on the controversy, Huawei also described events as an ongoing process.
Spark seemed dubious about whether Little's comments represented fresh hope.
"We would, of course, welcome any opportunity to achieve a different decision from the Government," a Spark insider told the Herald shortly after the GCSB Minister made his comments.
"That said, the fact we felt the need to make a market announcement yesterday should give you an indication, based on what we currently know of the GCSB position, of what we think are the prospects of changing that decision."
Yesterday afternoon, Spark pre-empted the government and GCSB by announcing the security agency's finding, and saying it could not now use Huawei gear for its pending 5G upgrade to its mobile network.
"The Director-General has informed Spark today that he considers Spark's proposal to use Huawei 5G equipment in Spark's planned 5G RAN would, if implemented, raise significant national security risks," Spark said.
"Under TICSA [The Telecommunications Interception Capability & Security Act], this means Spark cannot implement or give effect to its proposal to use Huawei RAN equipment in its planned 5G network."
Little maintained he had no issue with Spark going public with the diplomatically-sensitive development of the 5G ban. The telco was under a commercial obligation to disclose to investors.
The ball was now in Spark's court, he said.
"The role of the GCSB, at this point in the process, is to make an assessment when a telco wants to access new technology to their network. To access that against potential national security risks," Little said.
"That has been found in this case. That was what Spark was notified of yesterday.
"They [Spark] now have the option of coming back and working with the GCSB to see if it can mitigate those assessed risks ... That is the next part of the process if they choose to do that."
Little refused to say if the "significant national security risk" assessment was in part the result of intelligence about Huawei's alleged role in espionage, but he emphasised that it was a primarily a technical assessment.
Huawei said in a statement, "As the GCSB has noted, this is an ongoing process. We will actively address any concerns and work together to find a way forward."
Huawei says that it is a private company and is not controlled by Beijing. The deputy chief executive of its New Zealand operation, Andrew Bowater, has repeatedly told the Herald that no evidence has ever been tabled of Huawei posing a security threat.
Huawei currently provides network gear for Vodafone, Spark and 2degrees, as well as the Ultrafast Broadband (UFB) and Rural Broadband Initiative (RBI) rollouts.
Some commentators have said a finding against Huawei on 5G would mean that existing infrastructure would have to be ripped out - something that Telecommunications Users Association head Craig Young said would be an expensive and disruptive process.
But Little said that would not be necessary.
"The conventional [3G and 4G] technology has an infrastructure core and then peripheral technology such as cellphone towers and the like and they can - in effect - be kept separate, you cannot do that with 5G technology," he said.
Yesterday's development followed a US push, revealed on Friday, to persuade allies to drop Huawei.
But Little said this morning that the GCSB had arrived at an independent decision.
"I can say with considerable confidence that there's been no representations made to the GCSB from Australia, from the United States, from anywhere, about how it should go about making its decision," he said.
