Workers unload boxes containing the Sinopharm Covid-19 vaccine, donated by China, at the Damascus International Airport on April 24, 2021, in the Syrian capital.Loua Beshara | AFP | Getty ImagesU.S.-China competition may be heating up on another front: Covid-19 vaccine diplomacy.China has been a major Covid vaccine supplier to much of the developing world, an effort that some experts said could bolster Beijing’s global influence and deepen its ties with other nations.But a health governance and policy expert told CNBC on Thursday that the U.S. is now catching up, with the White House laying out plans to donate millions of Covid vaccine doses overseas and it appears President Joe Biden intends to do more.”We’re going to see that China is going to face a more formidable competitor,” Yanzhong Huang, senior fellow for global health at the Council on Foreign Relations, told CNBC’s “Squawk Box Asia.”In the last few months, China has been “almost the only primary player” sending Covid vaccines to other countries, said Huang, who is also a professor at Seton Hall University’s School of Diplomacy and International Relations.That’s especially so when India halted vaccine exports to prioritize its domestic needs and Russia’s supply overseas remains very limited, he explained.Several reports have pointed to the U.S. ramping up its effort to share Covid vaccines globally.Biden is reportedly set to announce in a speech at the G-7 summit on Thursday that the U.S. will buy 500 million more doses of the Pfizer-BioNTech vaccine to share with COVAX, a global vaccine-sharing initiative. CNBC also reported on Wednesday that the administration is negotiating with Moderna to secure additional vaccine doses to supply to the world.Origins of Covid-19Relations between the U.S. and China had been off to a rocky start under the Biden administration. The two sides have clashed on several issues, including the origins of the coronavirus, which was first detected in the Chinese city of Wuhan.Biden last month said he’s ordered a closer intelligence review of the pandemic’s origins, including whether the virus had escaped from a Chinese laboratory. In response, China accused the U.S. of a political “blame game.” Huang said the issue of Covid-19’s origins has become so politicized that it’s likely to stoke further U.S.-China tensions if additional evidence emerges to support the possibility that Covid-19 had originated from a laboratory incident.Without China’s cooperation, such “smoking gun” evidence may not be found, said Huang. Yet, in the West, the theory that the virus came from a lab has become an increasingly “credible, if not mainstream, explanation” of the pandemic’s origin, he said.