"The reality is that tensions between the United States and China are rising considerably at the moment," Willems, a former deputy director of the National Economic Council, told CNBC's "Squawk Box Asia."
"I know people get uncomfortable with the terminology, but I do think we have to be honest and call this what it is and this is the start of a new Cold War and if we're not careful, things could get much, much worse," he added.
Among the latest disputes between Washington and Beijing is the origin of the coronavirus, which has infected more than 3 million people and killed over 250,000 across 187 countries and territories, according to data compiled by Johns Hopkins University.
The virus first emerged in the Chinese city of Wuhan before spreading worldwide — and there's been growing outrage globally over how China handled its outbreak.
In the U.S., critics allege Beijing wasn't upfront about the dangers of the virus, was too slow to respond and under-reported the extent of the outbreak within its borders.
In the past week, President Donald Trump said he believed that China's "mistake" was the cause of the global pandemic, while Secretary of State Mike Pompeo said "a significant amount of evidence" suggested that the virus originated in a Wuhan laboratory.
China has rejected many of those claims and at times appeared to attempt to turn the tables around by alleging that the U.S. military might have brought the virus to Wuhan.
In an editorial published Monday, state media Global Times said Pompeo's accusation that the virus originated in a lab was "groundless." It also alleged that Pompeo was trying to vilify China to help Trump get reelected.
"The Trump administration continues to engage in unprecedented propaganda warfare while trying to impede global efforts in fighting the COVID-19 pandemic," the editorial read.
"The ultimate goal now is to win the election. If US public anger and dissatisfaction emerged due to Washington's incompetence over how it handled the pandemic, then the Trump administration would lose in November," it added.
Even within the U.S., there were claims that the Trump administration's rhetoric against China escalated during the pandemic because the president needed to find someone to blame for the weak economy going into the elections, said Willems, now a partner at law firm Akin Gump.
But such a statement is "a little too cute," he added.
"The reality is ... this has been coming a mile away, there's been growing frustration with China's economic policies and China has a lot to answer for when it comes to the coronavirus as well," he explained.
The U.S. and China had in the last two years engaged in a trade war, slapping significant amounts of additional tariffs on each other's products. That came after the Trump administration took aim at China's economic practices, including alleged intellectual property theft and favorable policies towards state-owned enterprises.
Willems, who left his position in the White House last year, was part of the U.S. negotiating team with China. He said that more tariffs — which Trump has reportedly threatened — is not the answer to many of the issues concerning China.
But he noted that the U.S. was also considering other options, such as an investigation into the origin of the virus and whether China did try to cover up the outbreak — and it's in China's interest to cooperate.
"I'm not one to peddle conspiracy theories but the reality is, if they have nothing to hide, why are they threatening to retaliate against Australia, why are they threatening to retaliate against the EU, the United States, who (are) simply saying there needs to be an investigation here," he said.
"I really think it would be in China's interest to kind of dial down these pressures and commit to international investigations," he added.