The Nerazzurri have started the season in relatively mediocre fashion, winning just three of their opening eight league games to be positioned 10 points adrift of leaders and reigning champions Juventus.
After scraping past Cesena with a 1-0 win on Sunday, Thohir appeared to be suggesting an ultimatum by saying: "We will see in the next two games... We want to give him another chance."
However, the Filipino businessman has attempted to sedate the notion that Mazzarri's days at San Siro are numbered by insisting the trainer has his complete support.
"My words were misinterpreted," Thohir told reporters on Monday. "I firmly believe in the work of the coach, the team and the future of this project.
"Nobody has given an ultimatum to Mazzarri although, of course, the results are important. Evidently, my words were poorly understood.
"I was very happy indeed with the win against Cesena and the character shown by the team."
Despite Thohir's stay of execution, rumours in Italy are swirling that Inter are planning to replace Mazzarri in the coming weeks, with Roberto Mancini the favourite to return to the club where he won numerous Scudetti as coach.
It has been a turbulent week for Inter behind the scenes, with former president Massimo Moratti resigning from his role as honorary president over unspecified disagreements with those now in charge at the San Siro club.