The UAW statement was the latest twist in a saga triggered by an online post by a man who claimed to work at Tesla's plant in California for four years and decried conditions faced by employees there.
Tesla co-founder and chief Musk was quoted at gadget review website Gizmodo this week as calling the accusations "morally outrageous" and saying it was his understanding the man was paid by the UAW to join Tesla and agitate for a union.
In a brief statement Friday, the UAW said the man "is not and has not been paid by the UAW" and called on Musk to apologize for spreading "fake news" about him.
The UAW confirmed that the post's author, who identified himself as Jose Moran, and others at Tesla have approached the union.
Moran contended that many Tesla workers put in more than 40 hours weekly of hard, manual labor, some of it "excessive mandatory overtime."
Machinery is not ergonomically designed to minimize risk of injuries, he maintained.
"I often feel like I am working for a company of the future under working conditions of the past," Moran said in a post at medium.com.
He also argued for a raise in pay, citing the high cost of living in the Silicon Valley area and contending that Tesla plant workers make a few dollars less hourly than peers in the automotive industry.
"In a company of our size, an 'open-door policy' simply isn't a solution," Moran said.
"We need better organization in the plant, and I, along with many of my coworkers, believe we can achieve that by coming together and forming a union."
Musk rejected Moran's claims about working conditions, according to Gizmodo.
In an email response to an AFP inquiry, Tesla said that as the largest manufacturing employer in California it has created thousands of jobs and "this is not the first time we have been the target of a professional union organizing effort such as this."
Tesla added that it has a history of engaging directly with employees about their concerns and will continue to do so "because it is the right thing to do."
The company's site in the northern California city of Fremont is the only car factory in the US where workers are not organized into unions.
The company making the software-infused electric cars, however, is also considered a member of a Silicon Valley technology world -- where skilled workers are not typically organized.
