The US President did not elaborate on what 6G might involve, with even his understanding of 5G appearing basic in a series of tweets on Thursday.
He described it as "far more powerful, faster and smarter" than current 4G technology, while also revealing his concerns that the US is lagging behind in the deployment of 5G.
"I want 5G, and even 6G, technology in the United States as soon as possible... American companies must step up their efforts, or get left behind," Trump tweeted.
Ren Zhengfei said the US was attempting to "crush" his company by encouraging allies not to use Huawei-made equipment.
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Trump's alleged efforts to shun Huawei all appear to stem from a US House Intelligence Committee report from 2012, which accused Huawei of having links with the Chinese government.
Government officials in the US have since been banned from using Huawei devices, with FBI Director Christopher Wray stating consumer handsets could be used by foreign governments to "maliciously modify or steal information."
US carriers have also faced pressure over their involvement with Huawei, meaning that despite being the second largest smartphone maker in the world, Huawei is yet to make any significant dent on the American market.
Huawei strenuously denies such allegations and claims that the US stance is motivated by trade policy rather than security fears.
Mr Zhengfei said this week that blocking Huawei would only serve to damage a country's technological development, stating: "The world cannot leave us because we are more advanced."
6G is anticipated to be another exponential leap, anticipated to arrive in 2030 or later.
Yet Trump's latest tweet suggests he might think the US can bypass Huawei by leapfrogging 5G and going straight to 6G.
"There is no reason that we should be lagging behind on something that is so obviously the future," Trump tweeted.
"I want the United States to win through competition, not by blocking out currently more advanced technologies. We must always be the leader in everything we do, especially when it comes to the very exciting world of technology!"
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