Fleming said that Britain's policy approach for 5G security was being concluded and that it would be announced by the minister responsible soon.
She said: "You can't just eliminate all risk by banishing one supplier".
The decision came despite opposition from key cabinet ministers.
The agreement reached at the NSC will be unveiled by the Department for Digital, Culture, Media and Sport "in the spring", according to May's official spokesman, although it is understood further work on safeguards needs to be done first.
"We're at a fork in the road". At the same time it also said that "no material progress has been made by Huawei in the remediation of the issues". The PM will no doubt be hoping that her partial ban is enough to avoid such an outcome.
"If that's the Government's choice then we need immediate clarity on what their plan B is to give us the 5G network our future prosperity demands".
"The National Cyber Security Centre is respected the world over, their advice is that we can manage/minimise any risk Huawei might pose to telecoms infrastructure and Theresa May is absolutely right to act on that advice".
Others, including the leadership candidates Jeremy Hunt and Sajid Javid, the foreign and home secretaries respectively, had raised concerns.
Downing Street declined to comment but Huawei welcomed the newspaper report.
Huawei is the leading manufacturer of equipment for next-generation 5G mobile networks with nearly instantaneous data transfer that will become the nervous system of Europe's economy, in strategic sectors like energy, transport, banking and health care.
The U.S.is keen that Five Eyes members do not involve Huawei in 5G development, as it could afford the Chinese Communist Party regime a back door to spy on their activities.
The UK will block Huawei from core parts of its 5G network and restrict its access to non-core areas, Reutersreported today, citing a security source.
Britain's move would be at odds with the United States, which has banned Huawei's 5G technology from its territory and urged allies in the so-called Five Eyes intelligence sharing collective - comprising also Australia, Britain, Canada and New Zealand - to follow suit.
With the new 5G standard set to be at the heart of many businesses and communications, security agencies and governments should be particularly choosy over the companies that are allowed to build this network.
"There's a reason others have said no".
At prime minister's questions on Wednesday, Julian Lewis, the chair of the defence committee, asked Lidington if ministers accepted Huawei was "intimately linked with the Chinese communist government and their deeply hostile intelligence services?"
A government spokesperson noted via email that the council's decisions are "confidential" and that the security of the country's telecoms network is "of paramount importance".
Member of civilian border group facing firearms charges
The federal agency said it had information at the time that that 20-member group was armed with weapons, including AK-47 rifles. Kraehe is leading the prosecution of the case, according to a written statement from the U.S.
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