The veteran centre-right politician, who took over past year with a promise to restore Brazil's stability after the impeachment of leftist president Dilma Rousseff, remained defiant.
In his statement Thursday, Mr Temer angrily responded to the claim, saying: "I never bought anyone's silence".
"I will not step down", he said after hours of consultations.
Temer - of the centre-right Brazilian Democratic Movement Party - took power in late August, after leftist Rousseff was removed from office for breaking budget laws.
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. He has promised to appeal if a court tries to remove him from office.
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 president is absolutely convinced he committed no crime, but that has to be made clear to the eyes of everyone'.
Days later, Loures was filmed receiving 500,000 reals (about 148,000 US dollars) in bribes from Batista.
Brazil's Treasury and central bank said they stood ready to keep markets liquid and working properly.
"All signs point to the end of the government: the opening of inquiry in the Supreme Court, allies abandoning the president, and critical media coverage", said Mauricio Santoro, a political scientist and professor of external relations at Rio de Janeiro State University. "He will likely lose all political support". "I know what I have done", he said, according to a BBC translation.
A one-time President Temer ally, Cunha was convicted on corruption charges relating to Brazil's sweeping graft probe known as operation "Car Wash".
Several hundred anti-Temer protesters gathered in São Paulo, while in the capital Brasília motorists honked horns and yelled "Temer out!".
The testimony states that a congressman, Rodrigo Rocha Lourdes, was sent by Temer to "resolve a matter" concerning a JBS subsidiary.
Temer's office denied the allegations, according to Reuters, but senior politicians immediately called for him to resign.
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.
He said the tape proved he had not approved bribing the witness, former lower house speaker Eduardo Cunha.
Cunha was arrested for several counts of corruption previous year, and threatened to tell the authorities what he knew about corruption schemes and bribery in the government.
Reports about Temer nearly pushed Trump off the front pages.
"Our entrepreneurial spirit and vast will to work in the face of a Brazilian system that presented us with several difficulties to sell our products, led us to make the choice to make inappropriate payments to public agents", he said in a statement Thursday.
A recent survey credited Temer with only 9 percent voter endorsement for performance - below Rousseff's standing at the moment of her suspension for allegedly masking data on the depth of the country's recession.
Protests were planned in the main cities across Brazil on Thursday night, many actually beginning shortly after Temer's refusal to resign was reported, with protesters calling for his ouster and direct elections.
The pressure built against Temer throughout the day. JBS was the biggest campaign donor that year for the re-election of Dilma Rousseff, as well as for the loser in the presidential race, Aecio Neves. The top court suspended Neves from the Senate.
- Installing Updates Can Stop Cyberattack — Microsoft Ransomware Patch
- Trump to embark on first overseas trip
- Media Stocks Slide As Investors Fear Turmoil From Trump Disclosures
- LeBron, Love help Cavs rout Celtics in Game 1
- Isco Says It Is Easy To Play With Cristiano Ronaldo
- Roger Ailes dead at 77, Fox News says
- Premier League don't care for clubs' welfare: Jose Mourinho
- UK's Liberal Democrats promise new Brexit vote if elected
- Advanced Micro Devices, Inc. (NASDAQ:AMD) Insider Watch on The Stock
- US House oversight panel head Chaffetz to leave Congress