A recording of the alleged conversation was presented to prosecutors by the chairman of JBS, the world's biggest meatpacker, as part of plea bargain negotiations, the O Globo newspaper reported on Wednesday.
According to the account, Temer authorised payments of hush money to Eduardo Cunha, a former speaker of the lower house who is in prison on charges of taking millions of dollars in bribes in the vast political embezzlement scandal at state oil firm Petrobras.
Temer's office immediately denied the report, adding that the president supported a full investigation of the allegations.
"President Michel Temer never solicited payments to obtain the silence of former deputy Eduardo Cunha," his office said a statement.
'Keep that up'
Cunha, once a powerful member of Temer's ruling party, has previously said he had compromising information about several senior politicians linked to the sprawling Petrobras scandal
According to O Globo, JBS Chairman Joesley Batista met with Temer on March 7, during which he secretly recorded himself telling the president that he was paying money to buy Cunha's silence.
Temer told Batista, "you need to keep that up, OK?", O Globo reported, without saying how it had obtained the alleged discussion.
Temer's office acknowledged the president had met with Batista, but said the conversation did not "compromise his conduct" as president.
O Globo's report, which three unidentified sources familiar with the matter told the Reuters news agency that it was accurate, threatened to pull Temer into a corruption scandal that has already entangled several of his closest allies and advisers.
Leading politicians and a third of Temer's cabinet have already been caught up in the investigation of systematic bribery in return for political favours and contracts with state-run enterprises.
But news that the president himself may have been party to a cover-up shook the scandal-weary nation.
"If the recordings are confirmed, Temer would have to defend his mandate in multiple fronts: public pressure for his resignation, an impeachment proceeding in Congress and an investigation by the general prosecutor's office," Thomas Favaro, an associate director at consultancy firm Control Risks, told clients in note.
“The development thus substantially increases the risk of an un-scheduled government change in Brazil before the 2018 general elections."
There were immediate demands for Temer's removal following O Globo's report.
Congressman Alessandro Molon, from the Rede party, filed a demand for impeachment with Rodrigo Mai, the speaker of the lower house.
The Workers' Party also issued a statement naming five other parties that called for his resignation and snap elections.
Beth Sahao, a Sao Paulo state lawmaker for the Worker’s Party, said the report confirmed what opponents had been waiting for: "Concrete evidence of corruption in the Temer government, but especially of the person of President Temer himself."
Several hundred anti-Temer protesters gathered in Sao Paulo, while in the capital Brasilia motorists honked horns and yelled "Temer out!"
Temer took office last year after President Dilma Rousseff was impeached on charges of breaking budget laws.
Author: News agencies