The NCSC's parent organisation, GCHQ, already carries out its own checks on Huawei's equipment.
A spokesman for Huawei declined to comment.
"What you're seeing here is that the UK government has finite resources," commented Alan Woodward, a former consultant to GCHQ.
"We could end up in a situation where the checks and balances needed to protect our security are insufficient, and effectively overwhelmed.
"Using yet more equipment sourced from China could mean that we open ourselves up to an unacceptable risk."
The US's action against ZTE stems from the fact the firm sold on US hardware and software to an Iranian telecoms carrier, in breach of sanctions imposed by Washington.
ZTE pleaded guilty to the offence last year and paid a $890m (£621m) penalty.
At the time the firm also promised to dismiss four senior workers and discipline 35 others. But it acknowledged in March that while it had fired the four managers, it had failed to keep the second part of its promise.
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