As part of the investigation, "controlled actions" - recorded conversations and exchanges of money which were tracked by federal police - were carried out.
Temer has denied any wrongdoing and on Thursday refused to resign.
FILE - In this May 12, 2016 file photo, Brazil's acting President Michel Temer whispers into the ear of Sen.
President Michel Temer delivers a statement on May 18, 2017 in Brasilia, Brazil.
Officers in the southern city of Curitiba searched the home of federal deputy Rodrido Rocha Loures, a longtime confidant of Temer and a member of the president's Brazilian Democratic Movement Party, or PMDB. The Brazilian Real lost 8 percent of its value against the United States dollar in the first half of the day.
Globo also reported that Mr Batista had recorded Mr Temer endorsing a bribe to silence Cunha.
Brazil's securities regulator has launched a probe into currency and stock trades made by executives at meatpacker JBS SA after they made plea bargain testimony that suggested Brazil's president had condoned bribery, Valor Econômico newspaper reported on Thursday, citing unnamed sources.
"I will not step down", he said in a short address on Thursday. Many have accused him of playing a role in engineering his predecessor's downfall for his own gain. At one stage São Paulo's main stock market index fell 10.7 percent triggering an automatic halt to trading. Brazil's currency, the real, lost 8 percent of its value against the US dollar.
Neves is being investigated in several corruption cases related to the "Car Wash" probe into kickbacks to politicians.
The O Globo newspaper reported on Wednesday night that Temer met in March with Joesley Batista, chairman of meat company JBS SA (JBSS3.SA), which grew rapidly under 13 years of leftist Workers Party rule due largely to low-priced loans from Brazil's national development bank.
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Temer spoke during a national address on Thursday afternoon.
Temer - of the center-right Brazilian Democratic Movement Party - took power in late August, after leftist Rousseff was removed from office for breaking budget laws.
Cunha led the impeachment fight that removed Dilma Rousseff from the presidency past year and put Temer, then the vice president, into power.
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 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.
Three people with direct knowledge of the investigation said the O Globo report was accurate.
"We need to see what the Supreme Court says and whether it accepts this tape as evidence", one presidential aide said. Globo did not say how it obtained the recording.
"There is no agreeing with payments for Eduardo Cunha", Marcio de Freitas, a spokesman for Temer said of the tape.
ELECTORAL COURT RULING The biggest threat to Temer's survival could be a ruling by Brazil's top electoral court, known as the TSE, annulling the results of the 2014 election won by the Rousseff-Temer ticket for the use of illegal funds in the campaign.
Both chambers of Congress were suspended amid the latest crisis in the government of less than a year.