The claims, published in The Wall Street Journal, presumably refer only to networks where Huawei equipment is used though the report was not specific about this point.
It said American officials had conveyed this information to their German and British counterparts late last year.
All telecommunications equipment makers are required to build into their hardware ways for governments to gain access for law enforcement reasons. The access can only be allowed by network operators at a telco, and the manufacturer is not allowed in by design.
In 2014, there were reports that the NSA had planted beacons in Cisco equipment in transit so that it would be possible to gain access to them once they were inside a network. The agency's Tailored Access Operations unit, now disbanded, was involved in the clandestine act which was detailed by the journalist Glenn Greenwald in his book No Place to Hide.
The WSJ report did not specify if US intelligence agencies had observed any Huawei intrusions into a mobile network. However, they said they had first observed the presence of backdoors in Huawei's 4G equipment in 2009.
For more than a decade, the US has been campaigning against Huawei. Recently, it has been trying to persuade countries it regards as allies not to use Huawei equipment in 5G networks. Only Australia has come out openly and said it would ban the Chinese firm from any role.
Washington claims that Huawei can be ordered to spy for the Chinese Government and is therefore a security risk. Huawei has strongly denied that it can be coerced into such activities.
Japan, Poland and South Korea have indicated that they would toe the US line but are yet to say so publicly.
Two weeks ago, the US suffered a blow to its efforts when the UK announced that it would allow Huawei to supply up to 35% of the gear for non-core parts of its 5G networks. Three UK telcos launched networks last year and all have used Huawei equipment in non-core parts of their networks.
Contacted for comment, a Huawei representative told iTWire the allegations had not been been backed up by any evidence, adding that Huawei's devices and networks were not a threat to the US or any country.
"In the 30 years since Huawei's founding, we have served over three billion people across 170 countries and maintained a spotless cyber-security track record," the representative added.
"Huawei has not had any major cyber security incidents while working with more than 500 telecom providers, including most of the top 50 telecom operators, for nearly 20 years in 170 countries to connect more than three billion people. No other vendor can claim this level of cyber security success.
"We have embedded strict security requirements into all of our systems used globally. We fully abide by all local laws and regulations in every nation we operate in.
"Currently, Huawei is the most scrutinised company in the world and has been taking measures to ensure the security of its products. Huawei R&D heavily focuses on security throughout the entire product lifecycle. Huawei has created testing centres in the UK, Brussels and Canada to allow for independent testing of Huawei's equipment. Huawei is investing an additional $2 billion to strengthen our
cyber security measures.
"Huawei has never received any request to add backdoors or spyware to its systems. Even if such a request was made, it would not be possible for Huawei to comply, as Huawei does not own or operate these networks nor does it have access to these network in the US.
"According to two independent, international law firms Zhong Lun and Clifford Chance, Chinese law does not compel Huawei to install so-called 'backdoors' in telecommunications infrastructure. The Ministry of Foreign Affairs of the People's Republic of China has also confirmed this claim is based on a misreading of China's National Intelligence Law.
"Clifford Chance reviewed an independent verification by Zhong Lun, which found the relevant articles of the Counter Espionage Law, the Anti-Terrorism Law, the Cyber Security Law, the National Intelligence Law, and the State Security Law do not empower PRC government authorities to plant so-called 'backdoors', eavesdropping devices or spyware in telecommunications equipment.
"When asked if China would request a company to spy on other countries, Chinese Premier Li Keqiang told reporters that "this is not consistent with Chinese law. This is not how China behaves...we did not do that and will not do that in future."
"Huawei has never received such a request and we would categorically refuse to comply if we did. Huawei is an independent company that works only to serve its customers. We would never compromise or harm any country, organisation, or individual, especially when it comes to cyber security and user privacy protection."