Musk said he and Maxwell just happened to be at the same party, and claimed Maxwell had "photobombed" him, reiterating a previous statement from a spokesperson.
"Ghislaine simply inserted herself behind him in a photo he was posing for without his knowledge," Musk's spokesperson told the New York Times.
In 2018, Epstein told a New York Times reporter he'd been contacted by a member of Musk's team for advice while Musk was under investigation by the Securities and Exchange Commission.
Both Tesla and Musk vehemently denied Epstein's claim and said it was "incorrect to say that Epstein ever advised Elon on anything".
Epstein and Musk have also attended dinners together in the past including one in 2011, according to a report by Buzzfeed News.
Musk once went to his house in Manhattan, according to ex-wife Talulah Riley, who also attended.
The photo of Musk and Maxwell was taken at an Oscars after-party in 2014 organised by Vanity Fair magazine.
Musk attended alongside his second (and then third) wife Riley, a couple of years before the pair divorced for the second and potentially final time.
Musk also denied rumours that Epstein had been given a private tour of SpaceX several years after his 2008 conviction for procuring an underage girl for prostitution.
Riley later tweeted to say she "wanted to respond publicly with Elon Musk's permission" given the "truly horrific nature" of the implications being drawn from the photo.
One implication she said she'd seen was that Maxwell had "procured" her as "some kind of child bride for Elon", which she denied.
"I don't know Maxwell," she said.
"Elon and I met when I was 22 and he was on a business trip to London. It was a chance meeting engineered by no one."
She said that, to her knowledge, she'd never met Maxwell, but conceded she might have been briefly introduced to her at some point during the 2014 party. She said it was unreasonable for everyone to remember all the people they've ever met, particularly with such high public profiles.
"Elon and I met thousands of people over the course of our relationship. There will be countless photos of Elon with people he doesn't know or happened to be stood next to at a party," Riley said.
She said a visit she and Musk paid to Epstein's Manhattan mansion was facilitated by a man taking them around the city and introducing them to various people, and she couldn't remember in what year it occurred.
Riley and Musk met in 2008, the same year Epstein was convicted, and it's likely the visit to the Manhattan house didn't happen until after he'd completed his sentence.
