The investigation raised the possibility Brazil could see a second president fall in less than a year.
The allegations of obstruction of justice against Temer caused Brazil's stock market to tumble on Thursday, with some analysts saying the president's woes would make it hard to continue his austerity drive, including an overhaul of Brazil's pension system.
In comments interpreted as being strongly supportive of Temer staying in office, he said that "in a situation like this, good sense, balance, calm are fundamental".
Brazil's top prosecutor has charged the President of the country with being a member of a criminal organization - just one of the jaw-dropping developments on Friday as the country's political crisis metastasized swiftly.
He spoke to the nation on Saturday.
Cunha has made claims alluding to the many secrets he knows that could help incriminate prominent politicians and businessmen, which seems to explain why Batista might have had an interest in buying his silence.
"No one has come to ask me to resign".
When the audio recording was released to the public on Thursday it did not appear to contain any explosive proof that Temer committed a crime.
In his speech Saturday, Temer lashed out at Joesley Batista, the JBS chairman, and other company executives, saying they were angry with his conservative government's austerity plans and efforts to curb the generous public financing of private companies that typified the administrations of his predecessors.
In it, two men can be heard talking about former Lower House Speaker Eduardo Cunha, now serving a 15-year prison sentence for corruption and money laundering.
The Supreme Court released the full contents of plea-bargain testimony from a pair of billionaire meat-baron brothers, whose decision to turn state's witness has created the most tumultuous moment in Brazil's modern political history.
A demonstrator holds a photo of Brazil's President Michel Temer that reads in Spanish "Get out Satan!" in Rio de Janeiro, Brazil, Thursday, May 18, 2017.More news: Maria Sharapova will not pursue Wimbledon wildcard after opting for qualification route
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Across the country, protesters Thursday night called for diretas já - "new elections".
But Mr Temer, who was vice-president until he came to power in a "legislative coup" that overthrew Workers' Party president Dilma Rousseff last August, refused to quit.
Brazil's Bovespa stock index lost 9%, its steepest fall since the 2008 financial crisis, on concerns the probe could derail Temer's fiscal reforms.
Brazil's Treasury and central bank said they stood ready to keep markets liquid before acting to smooth volatility in local currency and bond markets.
The corruption scandals that have polarised Brazil centre on political kickbacks in exchange for firms winning contracts at state-run enterprises, especially at oil company Petrobras.
As a powerful insider, Cunha has always been rumoured to be threatening to spill secrets on other politicians.
Adding fuel to the fire was the release yesterday of plea bargain testimony by executives at the huge JBS meatpacking company indicating that they had given Temer US$4.6 million (RM19.9 million) in bribes.
Temer, whose government has a 9% approval rating, had already been named in plea bargain testimony for negotiating millions in illegal campaign funding, which he denies.
The recording has led to calls from many corners for the 76-year-old career politician to resign.
Brazil's presidential system has no provision for calling elections before the end of the four-year presidential term, so this would require a constitutional amendment, a drawn out process which requires a three-fifths majority in Congress.
In light of the recordings, the Supreme Court suspended him from his position in the Senate and Neves' sister and cousin were arrested in connection by the Federal Police and his office in the Senate and his homes were searched by police.