Brazil's Bovespa stock market was briefly halted as investors reacted to corruption allegations against Brazilian President Michel Temer.
Demonstrators protest against Brazil's President Michel Temer in Sao Paulo, on May 17.
Mr Temer's office said he had never requested payments to Mr Cunha, and called for a full investigation into the allegations.
JBS, which grew rapidly under 13 years of leftist Workers Party rule due largely to low-priced loans from Brazil's national development bank, said on Thursday that it had no comment on the situation.
"If the recordings are confirmed, Temer would have to defend his mandate in multiple fronts: public pressure for his resignation, an impeachment proceeding in Congress and an investigation by the general prosecutor's office", Thomas Favaro, an associate director at consultancy firm Control Risks, told clients in note.
Last year, Temer took over as president after the impeachment of Dilma Rousseff in a ruction attributed to the then-powerful Cunha.
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The scandal started with Globo's report late Wednesday that Temer had been secretly recorded while talking to Joesley Batista, an executive from the meatpacking giant JBS, on March 7.More news: United States 'democracy is at risk' - lawmaker wants Trump impeached
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The veteran centre-right politician, who took over previous year with a promise to restore Brazil's stability after the impeachment of leftist president Dilma Rousseff, remained defiant.
Both JBS and its holding company, J&F, declined to comment.
Following Globo's report, Thursday began in a panic.
The prominent daily newspaper O Globo reported on Wednesday that a meat producer had recorded the President giving the go-ahead to bribe Cunha to "keep quiet" while he was in jail. Crowds also gathered outside the presidential palace chanting "Fora Temer" (Temer out).
The scandal is the latest shockwave from the wider "Car Wash" graft probe ripping through Brazilian politics, involving vast bribes and embezzlement. The former House Speaker was stripped of his parliamentary seat and jailed for corruption, money laundering and tax evasion.
A separate secret recording made by Batista allegedly caught Senator Aecio Neves, head of the PSDB party and a close Temer ally, asking him for a bribe of two million reais, or around Dollars 600,000. Aecio Neves, who almost won the presidency in 2014 and planned to run again next year.
According to Batista, Temer appeared to be satisfied with what was said, lowered his voice, and purportedly said, "Look, you've got to keep that up".
A major newspaper in Brazil, O Globo, is reporting that Temer was caught on tape discussing bribery payments. "He neither participated nor authorised any activity with the objective of preventing testimonies or cooperation with justice officials by the parliamentarian". With several ministers facing corruption allegations, they argue his government is no longer legitimate.
In addition to implicating Temer in the exchange with Cunha, Joesley Batista, the owner of JBS, reportedly testified that he had paid Cunha R$5 million since his imprisonment as part of an ongoing financial agreement, and still owed him R$20 million, in an agreement made after the politician exempted the poultry industry from certain taxes.