The action Wednesday is the latest in an ongoing clash between Huawei and the USA government, which claims the Chinese telecom company poses a threat to global cybersecurity.
Huawei began the campaign with an opinion piece in the Wall Street Journal Sunday.
According to Song, "The fact is, the USA government has provided no evidence to show that Huawei is a security threat".
The ban, along with separate accusations of bank fraud and corporate theft that the United States has made against Huawei and its chief financial officer, has exacerbated the trade war between Beijing and Washington.
Song said Huawei had agreed with the Justice Department that the challenge involved purely legal questions that could be decided in a simple court hearing. We have Western-based, rules-ordered, privacy-focused systems that we jointly engage in.
The firm also faces a broader USA executive order preventing the use of its equipment in the United States as well as the more damaging inclusion this month on an "entity list" that cuts it off from critical American-made components for its products, though a 90-day reprieve was issued.
Specifically, he called attention to Huawei's crucial role in providing affordable wireless services in rural America.
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He said Huawei's arguments, while strong on USA lawmakers' punitive intent, fall short constitutionally.
"There is no gun, no smoke - only speculation", he said today. "We hope that mistakes in the NDAA can be corrected by the court", Song added. The company said it would invest about $5 million in running 5G open lab in Seoul.
But countries including the US, Australia and Japan have moved to do the opposite by banning Huawei.
In line with a court scheduling order, a hearing on the motion is set for September 19.
If the threat from Huawei is real, what's the evidence?
"The bill directly determines that Huawei is guilty and imposed a large number of restrictions on Huawei", Song was quoted as saying.
It also called on the US government to halt its state-sanctioned campaign against Huawei because it will not deliver cybersecurity. The interview, taped Tuesday, aired on Fox Business Network Wednesday.
The lawsuit "will be an uphill battle because Congress has broad authority to protect us from perceived national security threats", said Franklin Turner, a government contracts lawyer at McCarter & English. For his part, Huawei's Liuping asserts that the government's policy will "directly harm more than 1,200 U.S. companies".
Huawei has been frequently been accused of wrongdoing, but not of the sort that makes it a national security risk.