While Ferrari is healthy economically, the F1 team have struggled in recent years and were a long way off the leaders at last weekend's home Italian Grand Prix, where there was a public spat over the performance of the team.

At the time, Montezemolo insisted he would stay on, but Marchionne said he was "terribly upset" by the F1 team's performance, which he had deemed "unacceptable".

The most successful team in F1 history, Ferrari have not won a constructors title since 2008 and this season have gone from bad to worse, with drivers Fernando Alonso and Kimi Raikkonen failing to win a single race.

"Our mutual desire to see Ferrari achieve its true potential on the track has led to misunderstandings which became clearly visible over the last weekend," Marchionne said.

Montezemolo joined Ferrari four decades ago after founding father Enzo Ferrari brought him in as his assistant. After a brief period away from the company, he returned as president in 1991 and over the past 23 years the F1 team have won 14 titles - eight constructors' championships and six drivers' titles (five won by Michael Schumacher and one by Raikkonen).

Matters came to a head at the weekend's race at Monza, when Alonso retired due to a rare mechanical problem and teammate Raikkonen struggled into a distant and uncompetitive ninth.

A Ferrari car had not retired for mechanical problems in 86 races and Sunday's results dropped Ferrari to fourth in the constructors standings behind Williams in third. Mercedes holds a massive 182-point lead in the team category ahead of Red Bull.