Ren Zhengfei described the arrest of his daughter Meng Wanzhou, the company's chief financial officer, as politically motivated.
The US is pursuing criminal charges against Huawei and Ms Meng, including money laundering, bank fraud and stealing trade secrets.
Ren dismissed the pressure from the US saying: "There's no way the US can crush us.. he world cannot leave us because we are more advanced. Even if they persuade more countries not to use us temporarily, we can always scale things down a bit."
He acknowledged that the potential loss of custom could have a significant impact.
"If the lights go out in the West, the East will still shine. And if the North goes dark, there is still the South. America doesn't represent the world. America only represents a portion of the world."
The UK's National Cyber Security Centre has decided that any risk posed by using Huawei technology in UK telecoms projects can be managed. Many of the UK's mobile companies, including Vodafone, EE and Three, are working with Huawei to develop their 5G networks.
They are awaiting a government review, due in March or April, that will decide whether they can use Huawei technology.
Ren said Huawei "won't withdraw its investment and will continue to invest in the UK.
"We still trust in the UK, and we hope that the UK will trust us even more.
"We will invest even more in the UK. Because if the US doesn't trust us, then we will shift our investment from the US to the UK on an even bigger scale."
Ren's daughter Meng Wanzhou, Huawei's chief financial officer, was arrested on 1 December in Vancouver at the request of the US, and is expected to be the subject of a formal extradition request.
In total, 23 charges are levelled against Huawei and Ms Weng. The charges are split across two indictments by the US Department of Justice.
Ren was clear in his opposition to the US accusations.
"Firstly, I object to what the US has done. This kind of politically motivated act is not acceptable. The US likes to sanction others, whenever there's an issue, they'll use such combative methods. We object to this. But now that we've gone down this path, we'll let the courts settle it."
Under Chinese law, firms are compelled to "support, co-operate with and collaborate in national intelligence work" but Ren said that allowing spying was a risk he wouldn't take.
"The Chinese government has already clearly said that it won't install any backdoors. And we won't install backdoors either. We're not going to risk the disgust of our country and of our customers all over the world, because of something like this. "Our company will never undertake any spying activities. If we have any such actions, then I'll shut the company down."