Temer immediately denied the report in O Globo newspaper.
According to the report, which could not be immediately verified, an executive from the meatpacking giant JBS, Joesley Batista, met with Temer on March 7.
During the meeting, the report said, Batista recorded himself telling Temer that he was paying money to buy the silence of disgraced ex-speaker of the lower house Eduardo Cunha.
Cunha is in prison after having been found guilty of taking millions of dollars in bribes in Brazil’s giant Petrobras oil company embezzlement scandal.
According to the account, Temer told Batista: “You need to keep doing that.”
Temer’s office issued a statement saying: “President Michel Temer never solicited payments to obtain the silence of former deputy Eduardo Cunha.”
Globo did not say how it got the information, which it said came from a plea bargain between Batista and his brother Wesley with prosecutors.
Temer took over last year after the impeachment of president Dilma Rousseff, a political earthquake to a large extent engineered by the then-powerful Cunha.
There were immediate demands late Wednesday from leftist opponents for his removal from the presidency.
Several hundred anti-Temer protesters gathered in Sao Paulo, while in the capital Brasilia motorists honked horns and yelled “Temer out!”
Congressman Alessandro Molon, from the Rede party, filed a demand for impeachment with the speaker of the lower house, Rodrigo Maia.
Maia, who would have to accept the demand for proceedings to start, made no comment to reporters as he left for an emergency meeting with the government, Globo reported.
“We came here after the accusations that came out… We already knew, but now there is a video, there is proof that the president committed a crime,” said protester Thiago Rocha, 33, in Brasilia.
“These people, like me, when they saw that on the news, they came here spontaneously, because they can’t take it anymore, we want democracy, we are outraged with this putschist president,” Rocha, a university professor, said.
The allegations in O Globo, which is part of the most powerful media group in Latin America’s biggest country, were a new shockwave from a corruption scandal tearing apart the country’s political elite.
Investigators mounting what’s called the “Car Wash” probe have uncovered gigantic embezzlement from Petrobras, with scores of politicians accused of taking bribes from executives in exchange for sweetheart contracts with the state-owned oil company.
Already a Who’s Who of the elite has been imprisoned or placed under investigation.
The accusations against Temer are especially explosive as he has been in power barely a year since the bitter maneuvers to push Rousseff out of office.
She was found guilty by Congress of illegally manipulating the government’s accounts to mask the depth of a painful recession. On being stripped of the presidency her vice president, Temer automatically took over.
Rousseff, from the leftist Workers’ Party, accused Temer and Cunha, from the center-right PMDB party, of mounting a coup.
Temer quickly set about introducing market reforms to try to get Brazil’s floundering economy back on the rails.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)