Despite calls for global cooperation, US and China fight over leading coronavirus response Other countries have called for a new global alliance to combat COVID-19.

The U.S. and Chinese governments have increasingly turned the novel coronavirus pandemic into a contest over their primacy as the world's leading humanitarian force, with Secretary of State Mike Pompeo highlighting U.S. contributions to global aid agencies Tuesday and pushing back on Chinese propaganda about its overseas assistance.

But as the pandemic spreads to the developing world and kills more people in nearly every region, experts say a lack of global coordination has cost the world time, money, and lives, with some saying U.S. leadership has been missing.

"This pandemic can only be won when countries and means and resources are put and pooled together to contain and to fight the spread of the virus," Robert Mardini, director-general designate of the International Committee of the Red Cross, told ABC News. "This is the only way forward."

Pompeo has consistently taken China to task as Chinese officials have spread false information about the U.S. being the source of the novel coronavirus, with a Chinese Foreign Ministry spokesperson even pushing the conspiracy theory that the U.S. military brought it to Wuhan -- the Chinese city of 11 million where cases first exploded.

But that diplomatic spat seemed to recede in the last week. President Donald Trump largely stopped using the phrase "Chinese virus," saying he didn't "need" to anymore, and during a briefing at the State Department Tuesday, Pompeo didn't use the phrase "Wuhan virus" either, which a State Department official had told ABC News he used to push back on Chinese disinformation.

That's because Chinese propaganda organs had stopped pushing that conspiracy theory, according to Lea Gabrielle, head of the State Department's Global Engagement Center, which monitors and combats state-run and terrorist recruitment propaganda. After receiving a negative response in Latin America and Africa, according to Gabrielle, China's state-run media outlets, amplified by their overseas ambassadors, have shifted to focus on propaganda praising the Communist Party's response and criticizing the U.S. for stigmatizing China.

Pompeo seemed to take aim at that Tuesday, telling reporters, "The United States was one of the first nations to step forward and offer help. ... We've long maintained an unsurpassed commitment to global health and humanitarian assistance."

The State Department followed up by issuing a fact sheet Tuesday, showing how U.S. contributions to global agencies far surpass China's -- $400 million to the World Health Organization, compared to China's $44 million; $700 million to UNICEF, compared to China's $16 million; and $1.7 billion to the United Nations High Commissioner for Refugees (UNHCR), compared to $1.9 million from China.

Senior U.S. officials have also accused the Chinese government of attaching "strings" to their assistance.

"The Chinese Communist Party has a special responsibility to provide no-strings-attached assistance around the world and take responsibility for what everyone realizes is the result of the cover-up that happened in Wuhan," James Richardson, director of the State Department's office of foreign assistance resources, said Thursday, although he did not provide evidence of China attaching any conditions to its aid.

Instead, some countries have welcomed Chinese assistance and praised Beijing for providing much-needed medical supplies or sharing data and know-how. Ethiopia's health minister thanked Chinese officials for "sharing valuable experience" and helping "improve the capacity of Africa in containing COVID-19," while the African Union's commissioner of social affairs praised Chinese "cooperation ... to fight COVID-19 in the continent," including the supply of more than 10,000 lab testing kits.

But other countries have pushed back on Beijing, reporting that Chinese-provided tests or other medical supplies have been defective. The Dutch Health Ministry said over the weekend that 600,000 medical masks from China would not be used and some would be recalled after distribution because they did not fit or work properly. In Spain, health authorities said tens of thousands of tests, out of hundreds of thousands from China, were defective, with Turkey and the Czech Republic reporting similar issues.

The European Union's top diplomat, Josep Borrell, warned that the U.S. and China are competing in "a struggle for influence through spinning and the 'politics of generosity.'"

"China is aggressively pushing the message that, unlike the U.S., it is a responsible and reliable partner. In the battle of narratives, we have also seen attempts to discredit the EU as such, and some instances where Europeans have been stigmatized as if all were carriers of the virus," Borrell said, an apparent reference to Trump's restriction on travel from Europe that he initially cast as a Europe-wide ban and that was issued without European consultation, a senior European diplomat told ABC News at the time.

Pompeo's statement also seemed intended to quell a domestic audience. With testing insufficient to broadly trace and isolate cases in the U.S., and shortages of equipment like face masks and ventilators putting the lives of medical professionals and patients at risk, there has been anger over U.S. assistance to other countries.

In particular, the State Department helped send 17.8 tons of personal protective equipment, or PPE, and other medical supplies from U.S. charities, including Samaritan's Purse and the Mormon Church, to Wuhan in early February. Pompeo tweeted video of their arrival in China, saying they "can help save lives in #China and help protect people from the #coronavirus."

"Trump, you incompetent idiot! You sent 18 tons of PPE to China early but ignored warnings & called COVID19 concerns a hoax. You've endangered doctors, nurses, aids, orderlies, & janitors - all risking their lives to save ours," tweeted Rep. Maxine Waters, D-Calif., chair of the House Financial Services Committee -- although those supplies didn’t come from the nation’s stockpiles.

The U.S. has offered $274 million to assist 64 different countries and UNHCR in combatting the pandemic, and Pompeo said Tuesday those funds are key to keeping the American people safe as well.

"In America, we provide aid because we're a generous and noble people. We also do it because we know from prior experiences that [if] we don't have good data, full transparency, and all-out effort to fight pandemics, that can harm Americans back home, too," he said.

But experts have called for a global effort to combat the pandemic, arguing that individual countries alone, battling over medical resources or finger-pointing about the virus' origins, will not solve this crisis. The U.S., however, has made no public effort to bring together like-minded countries, and foreign ministers from the G7 alliance of democracies failed to issue a joint statement on the pandemic after Pompeo insisted the group call it the "Wuhan virus."

"Unfortunately, even as COVID-19 accelerates inside our country, the Trump administration seems to view diplomacy as a bludgeon to score points against adversaries and alienate friends rather than an essential tool for helping to protect Americans," tweeted Brett McGurk, a senior diplomat under George W. Bush and Barack Obama who served as special envoy to the Global Coalition to Defeat ISIS until he resigned over Trump's ordered withdrawal from Syria.

The presidents of Germany, Singapore, Ethiopia, and Ecuador, and the king of Jordan authored a joint op-ed in the Financial Times on Tuesday, calling for a new global alliance to convene the "medical, economic, and political elements required to produce a vaccine for all who need it" and ensure that testing kits are produced quickly and distributed widely and fairly.

"This is a global crisis. Delay in action means death. We all face the same enemy and we stand to gain by bringing the full force of humanity together to fight it," the five leaders wrote. "Before this virus, we are all equal and must work together to beat it."

ABC News's Mel Madarang contributed to this report.

What to know about the coronavirus:

How it started and how to protect yourself: Coronavirus explained

What to do if you have symptoms: Coronavirus symptoms

Tracking the spread in the U.S. and worldwide: Coronavirus map

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