Former Napoli boss Mazzarri's role at San Siro was rumoured to be under threat following Inter's 3-1 defeat to Serie A leaders Juventus on Sunday.
The result dropped sixth-placed Inter out of the UEFA Europa League places by virtue of Verona's 2-1 win at Sassuolo.
Inter are winless in their last six games in all competitions, but president Thohir, who took over the club last October, is staying patient in what he described as a "transition year".
In a statement released on Inter's official website Thohir said: "We are going through a transition year and our main aim is to lay the foundations for our future: this is a difficult season and clearly it is not easy to find another winning combination like the one we had a few years ago.
"This is why we must be patient and move forward with a clear vision focusing on two basic concepts: how to improve our performance on the pitch and how to build our team for the future.
"To achieve the first target we have hired one of the best Italian coaches in circulation, Walter Mazzarri, with whom we are working for the present and planning for the future.
"The signings of Hernanes and (Danilo) D'Ambrosio - chosen by myself, our management and the coach in unison - are indicative in that sense: two key players who can help this club get going again. They will undoubtedly contribute greatly both this year and in the coming seasons."
"Regarding the future it's important to stress that we have not yet taken any decisions about the players who currently make up our roster: the coach's assessment at the end of the Serie A season will be decisive in that respect.
"I will sit down and discuss with him which players possess the necessary qualities and motivation to remain with us, and which players are to make way for new faces."
