On Saturday, the Agnelli family's holding company Exor rejected an all-cash offer from crypto firm Tether to buy its entire stake in Italy's most successful club.
"Juve has been part of my family for 102 years," Exor CEO Elkann said in a video on Juventus' website.
"Juve is part of a much, much larger family, the Bianconeri family, made up of millions of fans in Italy and around the world who love Juve the way you love the people closest to you.
"It is with this passion in mind, with this love story that has united us for more than a century, that as a family we continue to support our team and look to the future to build a winning Juve."
Juventus won the last of their 36 top-flight titles in 2020 - their ninth consecutive Scudetto triumph - and have since failed to really challenge for the Scudetto, overtaken by the likes of Inter and AC Milan, along with Napoli.
Spalletti joined the club at the end of October and is the fifth manager appointed since that last success, but there is little sign of an upturn in fortunes with Juve currently seventh in the standings and eight points off leaders Milan.
"Even though I've only been here a short time, I think I can include the whole squad in this conversation," Spalletti told a press conference ahead of Sunday's game at Bologna.
"It's gratifying once again to hear the strength and passion that John Elkann and the family have for this club.
"It's clear that it's up to us to give substance and solidity to that passion, by honouring the past and building a future at the same level, or even better."
Spalletti has signed a contract until the end of the season, and if the title appears to be slipping out of reach, securing a place in next season's Champions League would likely be the minimum required to earn a renewal.
Since Spalletti's arrival, Juventus have won two of five league matches to slide further away from the summit, but the manager refused to believe he did not have a strong enough squad to turn things around.
"No one will convince me that these players aren't good. On the contrary, I'm convinced we will overcome these limitations," Spalletti said.
"I accepted this role because I believe in it. I've been doing this job for years, and I know it isn't easy. I'm obsessed with the idea of being able to change and improve this group."
Bologna are in fifth place, two points ahead of Juve.