"This never happened. Not at this meeting nor at any other which I held during my public life with any person or legal entity. I would never put my reputation at risk," he said in a video address yesterday.
This week, a Supreme Court justice opened corruption probes into almost 100 politicians, including many close to the president.
Temer is not being targeted in any investigation because he has immunity while in office.
Former Odebrecht executive Marcio Faria told prosecutors as part of a plea bargain that his company made the deal to win a contract with state oil enterprise Petrobras. The amount was allegedly USD 40 million, or five per cent of the contract's value.
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"It was clear that we were talking about a bribe," Faria said in his testimony.
Temer responded Wednesday in a written statement, then took the unusual step of making a second statement in a short video address yesterday.
"But it is a lie that in our meeting I would have heard reference to financial amounts or scandalous business between the company and politicians."
"My greatest ally is the truth, the raw material of the justice system, which will reveal all the truth of the facts.