"The rumor that Bill Gates [and] I are lovers is completely untrue," Musk wrote.
Musk also tweeted, "Billy G is not my lover," in response to a tweet sharing a Tuesday comment from Gates about Musk.
"Elon's positioning is to maintain a high level of outrageous comments," Gates said in a CNBC interview. "He's not much involved in vaccines. He makes a great electric car. And his rockets work well. So he's allowed to say these things. I hope that he doesn't confuse areas he's not involved in too much."
Gates, who has been vocal about the Unites States' handling of the coronavirus and the importance of developing effective vaccines, made the comments after Musk posted a June 30 tweet suggesting that many positive COVID-19 tests could be false.
"There are a lot of [COVID-19] false positives messing up the numbers. Even tests with 5% false positive rate (in *field*, not lab) would show up as ~17 million fake [COVID-19] cases even if there were actually none," he wrote.
It's not the first time Musk has shared a controversial opinion regarding COVID-19. The Tesla founder brushed off virus fears as "dumb" on March 6 and took some flak for tweeting that children are "essentially immune" to COVID-19.
Gates has donated hundreds of millions of dollars to COVID-19 relief efforts, and Musk has donated personal protective equipment (PPE) and ventilators to hospitals across the country.