The board, including Chairman Andrea Agnelli and CEO Maurizio Arrivabene, resigned on Monday as prosecutors and Italian market regulator Consob look into the club's affairs over alleged irregularities linked to player transfers and wages.
"We are counting on him (Allegri) and the whole team to continue winning as they have shown they can do in the last few games, keeping our goals high on the pitch," Elkann said.
In a short statement, Allegri said his sole focus was on the pitch and the team while thanking Elkann for the support.
"It's always very positive to feel the closeness of the shareholders, so I thank John Elkann for these words," he said.
Allegri won five Serie A titles, four Italian Cups and two Italian Super Cups as well as taking Juve to the Champions League final twice during his first spell in charge from 2014-19 before he returned to take the reins again in 2021.
"In these years of work, passion and victories I have always been able to count on the support of Andrea Agnelli, to whom I am bound by a relationship of friendship, which will not be interrupted with the end of his presidency.
"Andrea and John are reference figures for the Juventus world that must remain focused on the daily work on the pitch to obtain the results we all want."
Third-placed Juve won a sixth straight Serie A game before the World Cup to reach 31 points -- one more than fourth-placed Lazio and Inter Milan in fifth but 10 adrift of leaders Napoli.
Juventus resume their campaign at Cremonese on January 4.
