A poor run has led to widespread speculation over Mazzarri's future and the names of Sampdoria coach Sinisa Mihajlovic, Udinese's Andrea Stramaccioni and former Everton and Manchester United boss David Moyes have all been churned up by the rumour mill as possible replacements.
A controversial 1-0 win at Cesena on Sunday, however, eased the pressure and Thohir denied in a statement that Mazzarri had been given any ultimatum, contradicting earlier comments attributed to him in his native Indonesia.
"When I was in Italy on my last trip, I explained and stressed several times how much I believe in our coach and the team, in this project," said Thohir on Inter's website (www.inter.it).
"I'll say it again now. Obviously results are important but we're not counting down games for anyone, clearly some of what I said has been misinterpreted.
"I'm very happy with yesterday's result, the team played with heart and determination. I hope we consistently see performances like that."
Earlier, Thohir had told Indonesian media that he was still mulling over Mazzarri's situation.
"We have to be fair to the coach. We'll see in the next two games, although changing the coach is not a good solution," he was quoted as saying.
"We'd like to give him the opportunity first. There have been lots of rumours about coaches, and obviously we will find the best coach for Inter."
Inter's three previous league games were a 4-1 home defeat to Cagliari, a 3-0 loss to goal-shy Fiorentina and a 2-2 draw with Napoli, and Mazzarri said the players clearly felt the pressure on Sunday.
“We really needed this win," said the irascible former midfielder, adding that he would rather have played the whole match against eleven men.
“I know they were desperate to win and prove themselves, but at times you have to be calmer and take your time and make the right decision.
"We could have had tried more long-range shots but they sometimes seemed determined to walk it into the net."
"If Thohir wants me to stay, that's fine, if not, I'll be on my way," he added. "That's how it's always been in football."
Inter are joint eighth alongside Genoa with 12 points from eight games while Sampdoria are joint third with 16.
Genoa host leaders and defending champions Juventus, who have dropped only two points, while AS Roma, who are three points behind in second, entertain promoted Cesena in two of Wednesday’s other games.
(Writing by Brian Homewood in Berne, editing by Julien Pretot/Rex Gowar)
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