The top US diplomat's sharp words underscored criticism from other members of the Biden administration over Beijing's lack of transparency in the crucial early days of the pandemic.
The countries' joint statement supported further studies of animals to find how the virus was introduced to humans.
"I do not believe that this assessment was extensive enough."
The report is "extremely sensitive" to China, which has consistently claimed that it is not responsible for the spread of the coronavirus.
One 49-year-old woman died as a result of severe coagulation disorders, while a 35-year-old woman developed a pulmonary embolism and is recovering.
He urged health authorities to listen to patients' concerns, take them seriously, and establish services to help them.
The study showed there were around 6,000 additional deaths in Wuhan over the January-March 2020 period, including 4,573 caused by pneumonia — most of which were COVID-related.
Blinken noted that the US plans to provide significant financial support to COVAX through Gavi, the Vaccine Alliance.