Mr Temer is trying to get pension reforms through Congress that would mean men would have a minimum retirement age of 65, and women 62, and most people would contribute more.
His statement followed one of the most chaotic sessions for the country's financial markets since the global financial crisis, with stocks on its benchmark Ibovespa falling more than 8% and the real plunging 7.5% against the USA dollar, the most since 1999, despite the intervention of the central bank of Brazil. The Brazilian Real lost 8 percent of its value against the U.S. dollar in the first half of the day.
The scandal deepened as police searched the Rio de Janeiro home and Brasilia office of Senator Aecio Neves.
The recordings also implicate senator and former presidential candidate Aecio Neves, who reportedly asked Batista for almost $600,000 to pay for his defense in the Car Wash Corruption Probe.
Temer denied the accusations and after much speculation told an audience on Thursday in the capital Brasilia he would not resign.
Late Wednesday, Globo reported that Neves had been recorded asking JBS meat-packing company executive Joesley Batista for $700,000 to pay for his "Car Wash" defense.
"I will not resign", Temer said in a televised message to the nation after the Supreme Federal Court chose to open an investigation regarding allegations made the previous day that he approved of payments to a former powerful lawmaker to keep quiet.
Less than 24 hours after O Globo newspaper's explosive report that Temer had been caught on tape agreeing to bribe the jailed politician, he faced three formal requests for his impeachment.
Cunha, formally of Temer's Brazilian Democratic Party (PMDB), led the impeachment charge against ex-president Dilma Rousseff that culminated in Temer taking power.
Brazil was one of the best-performing markets of 2016 with the MSCI Brazil index returning 66% during the year on the back of ambitious reform plans and rising commodity prices. Rousseff and Temer are on trial in a case separate from the Car Wash investigation, for allegedly accepting illegal donations as part of their 2014 campaign.
Cunha led the impeachment fight that removed Dilma Rousseff from the presidency a year ago and put Temer, then the vice president, into power. Aecio Neves, who almost won the presidency in 2014 and planned to run again next year.
As traders and exchange operators tried to reassess the volatile situation, Brazil's Central Bank (CB) issued a statement to try to calm foreign and domestic investors by insisting that the political turbulence would not significantly affect the country's economy.
"Michel Temer is like that boyfriend who doesn't know it's over", one Twitter user said. Cunha was later imprisoned on a 15-year sentence for corruption. The Podemos party said Thursday that its 13 members in the lower house have left the governing coalition.
At the same time, a massive corruption scandal involving the state oil company Petrobras was unfolding.
Demonstrators shout slogans against Brazilian President Michel Temer in Sao Paulo.
"This climate isn't one in which to work", Rodrigo Maia, president of the lower chamber, told Globo News.
Globo's report had an immediate impact. Queiroz said that after that denunciation, Temer is pressured by society - on the ethical side - and also by the market that was supporting the government, because he is no longer able to offer what he promised.
PSDB Social Democrat leader Ricardo Tripoli said: "If the evidence is confirmed, then we will ask our (ministers) to leave the government".