"I will not resign," he announced emphatically in a brief televised statement to the nation.
Less than 24 hours after an explosive report in O Globo newspaper that Temer was caught on tape agreeing to bribe the jailed politician, he faced three formal requests for his impeachment.
There were also signs that his ruling coalition was crumbling, with some allies calling for his resignation.
Piling on the pressure, the Supreme Court gave its green light to the opening of a formal investigation into Temer's alleged involvement with the hush money.
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However, the veteran centre-right politician, who took over last year with a promise to restore Brazil's stability after the impeachment of leftist president Dilma Rousseff, came out swinging.
He highlighted signs this week that Brazil's two-year recession is coming to an end and claimed that "optimism was returning" thanks to a programme of austerity reforms that he is trying to pass in Congress.
Now "those efforts may come to nothing", he warned.
It remained unclear whether Temer's defiance will be enough, with cracks growing in the ruling coalition, which is centred on Temer's PMDB party and the PSDB Social Democrats, along with a coalition of smaller parties.
Senator Randolfe Rodrigues from the opposition Rede party promised demonstrations until Temer quits.
"Brazil has no government," Rodrigues said.
The Sao Paulo stock market reacted in panic to the spectre of Brazil losing its second president in just over 12 months.
The Bovespa index crashed more than 10 per cent after opening, triggering an automatic suspension of trading for 30 minutes.
Investors have been counting on Temer pushing through the austerity reforms, which include a raising of the minimum retirement age, so that Brazil's bloated public finances can be brought under control.
According to the report, the president discussed the matter with Joesley Batista, an executive from the meatpacking giant JBS, on March 7.
Batista told Temer that he was paying money to make sure that Cunha -- thought to have encyclopedic knowledge of Brazil's notoriously dirty political world -- would keep quiet while serving his jail sentence for taking bribes.
In the recording, offered as evidence in a plea bargain between Batista and his brother Wesley with prosecutors, Temer allegedly can be heard telling Batista: "You need to keep doing that, OK?"
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 USD 600,000.
The Supreme Court suspended Neves. Officers could be seen entering Neves' property in Rio de Janeiro and his sister Andrea was arrested in Belo Horizonte.
Globo published what seemed to be pictures showing men delivering a suitcase of cash for Neves.
The scandal is the latest shockwave from the wider "Car Wash" graft probe ripping through Brazilian politics.
Former president Luiz Inacio Lula da Silva, a leftist icon for many in Latin America, faces five corruption trials, while a third of the Senate and a third of Temer's own cabinet are under investigation.
Until now Temer has managed to stay above the fray.
Although previously alleged to have participated in large-scale bribery deals, Temer had limited immunity.