"I will not resign. I repeat: I will not resign," he announced angrily, wagging his finger, in a brief but televised statement to the nation.
Temer's combative reaction was followed shortly after by street demonstrations in Rio de Janeiro, Sao Paulo and the capital Brasilia demanding his resignation.
"Temer out!" chanted several thousand protesters in Rio, also calling for snap elections.
Around 24 hours after an explosive report in O Globo newspaper that said Temer had been caught on tape agreeing to bribe the jailed politician, he faced eight formal requests for his impeachment.
There were also signs that his ruling center-right coalition was crumbling, with some allies calling for his resignation. The culture minister, Roberto Freire, resigned and there were indications that the urban affairs minister would follow.
Piling on the pressure, the Supreme Court greenlighted a formal investigation into Temer's alleged involvement with the hush money.
There had been speculation that Temer would use his televised address to resign. Instead, the veteran center-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 program of austerity reforms that he is trying to pass in Congress.
Now "those efforts may come to nothing," he warned.
Stock market plunge
It remained unclear whether Temer's defiance will be enough, with cracks growing in the ruling coalition, which is centered on Temer's PMDB party and the PSDB Social Democrats, along with a coalition of smaller parties.
Earlier, a PSDB leader, Ricardo Tripoli, told AFP that "if the evidence is confirmed, then we will ask our (ministers) to leave the government."
The Sao Paulo stock market reacted in panic to the specter of Brazil losing its second president in just over 12 months.
The Bovespa index crashed more than 10 percent after opening, triggering an automatic suspension of trading for 30 minutes. It closed 8.8 percent down.
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.
Suitcase of cash
Temer was reported late Wednesday by O Globo to have been secretly recorded agreeing to payments of hush money to Eduardo Cunha, the disgraced former speaker of the lower house of Congress.
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?"
In his statement Thursday, Temer angrily responded to the claim, saying: "I never bought anyone's silence."
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 $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.
Investigators have uncovered a massive scheme in which politicians took bribes in exchange for getting big businesses overinflated contracts with state oil company Petrobras. The bribery and embezzlement then rippled far beyond, pulling in many of the country's most famous executives and leaders.
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.
He could not be prosecuted for crimes prior to his mandate. However, the hush money claims date from well within his time in office.
If he resigns he would no longer have his case handled by the Supreme Court, but be moved to what are seen as far more aggressive, quicker-acting lower courts.
If he stays, Congress could launch impeachment proceedings but that would depend on him losing his base.
"That's why today the main question is to know whether the parties that form the government's base will leave," said Thomaz Pereira, constitutional law professor at the Getulio Vargas Foundation in Rio.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)