Temer strongly denied allegations of wrongdoing and told allied lawmakers in a morning meeting that he would not be driven from office.
"If Temer doesn't fall, he will lead a walking dead administration", said Claudio Couto, a political science professor at Fundacao Getulio Vargas, a Sao Paulo-based university and think tank.
On Thursday, the Supreme Court launched an investigation into Temer and he faced four separate impeachment requests in Congress.
Mr Temer is already deeply unpopular in Brazil but his centre-right party has been able to govern as part of a coalition.
"We need to see what the Supreme Court says and whether it accepts this tape as evidence", a presidential aide said.
"I will not resign, I repeat, I will not resign".
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Globo did not say how it got the information about the recording, which it said was offered in a plea bargain between Batista and his brother Wesley with prosecutors.
Shares of state-controlled companies, such as Banco do Brasil SA and Centrais Elétricas Brasileiras SA, or Eletrobras, lost about a fifth of their value, and the nation's currency fell 7.5%, wiping out its gains for the year.
Some Temer allies tried to shore up confidence, but others said his Brazilian Democratic Movement Party, or PMDB, was in tatters.
The scandal has engulfed Brazilian politics, with a third of Mr Temer's cabinet under investigation for alleged corruption.
Explosive tapes of Temer's discussions about hush-money payments to jailed powerbroker Eduardo Cunha have been found. Eduardo Cunha, the former speaker of the House had been jailed for his role in the Petrobras corruption scandal. Loures was then filmed receiving 500,000 reals ($160,000) in bribes from Batista.
Late Wednesday, Globo newspaper reported that Neves was recorded asking JBS meat-packing company executive Joesley Batista for $700,000 to pay for his "Car Wash" defense.
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Three people with direct knowledge of the investigation said the O Globo report was accurate.
JBS, which grew rapidly under 13 years of leftist Workers Party rule due largely to low-priced loans from Brazil's national development bank, on Thursday said in a statement that seven of its executives, including Batista, had reached plea bargain deals with prosecutors.
If President Temer is eventually forced to resign or is impeached, Brazil's constitution calls for the leader of the lower house to temporarily take over and for Congress to name a successor within 30 days.
However, he dismisses his rock bottom popularity ratings, saying that as an unpopular president due to rule only until the next scheduled elections in October 2018 he is free to push ahead with the painful austerity reforms the country needs.
Activist groups from across the political spectrum took to social media, calling for protests this weekend. The Supreme Court suspended Neves from the Senate.
Neves almost won the presidency in 2014 and had planned to run in 2018. Instead, the veteran center-right politician - who took over previous year with a promise to restore Brazil's stability after the impeachment of leftist president Dilma Rousseff - came out swinging.
Chelsea Manning has been liberated
Under this status she will not receive pay but is entitled to medical care at military facilities and other military privileges. There's so much wrong with this, I don't know where to begin. "Whatever is ahead of me is far more important than the past".
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