"Something extremely bogus is going on. Was tested for covid four times today. Two tests came back negative, two came back positive. Same machine, same test, same nurse. Rapid antigen test from BD," Musk said in a tweet, referring to Becton Dickinson and Co's rapid antigen test.
Musk, who took rapid antigen tests on Thursday, said he was also awaiting results from polymerase chain reaction (PCR) tests from different labs.
When asked by a Twitter user if he showed any symptoms, Musk said he had symptoms of a "typical cold".
"Nothing unusual so far," Musk added.
Becton Dickinson, which is one of the major suppliers of COVID-19 antigen tests, said in September it was investigating reports from U.S. nursing homes that its rapid coronavirus testing equipment was producing false-positive results.
"We are aware of the tweet by Elon Musk and are reaching out to learn more, consistent with our quality management process," the company said in a statement on Friday.
"While the scientific community agrees that no diagnostic test is perfect, we stand behind the quality, utility and science of our system and assay."
Earlier this month, the U.S. Food and Drug Administration said it was alerting clinical laboratory staff and healthcare providers that false positive results can occur with COVID-19 antigen tests.
Musk had previously criticized coronavirus-related restrictions and lockdowns, referring to those as "fascist" and an infringement on individual liberty.
Becton Dickinson did not respond to a request for comment late on Thursday.
(Reporting by Kanishka Singh in Bengaluru; Editing by Rashmi Aich and Anil D'Silva)
