Temer and a senior senator, Aecio Neves, were among those "who attempted to prevent the Car Wash investigations from advancing", Prosecutor General Rodrigo Janot wrote in a court filing that was made public today.
The accusation of wide-scale obstruction of justice raised the stakes in a crisis threatening to topple Temer barely a year after the centre-right politician took over from impeached leftist president Dilma Rousseff.
Temer was placed under investigation yesterday over a secretly recorded conversation with a business executive in which the president is purported to have given his blessing to monthly payments of hush money to a jailed politician.
The investigation has upended Brazil with scores of politicians indicted or subject to probes into alleged bribe taking and embezzlement. And Cunha, formerly one of the most powerful insiders in Congress, has long been rumoured to have threatened to spill secrets on other politicians to prosecutors.
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Temer angrily denied any wrongdoing in a televised address yesterday and rebutted mounting calls for his resignation. He had not spoken in public today.
The beleaguered president was holed up at the presidential palace with close aides, a government source, who asked not to be identified, told AFP.
According to the source, Temer was "angry" and had no intention of stepping down.
However, opponents piled on the pressure, with eight impeachment requests filed in Congress.
There are also calls for large-scale street protests to demand his resignation.
Temer's conservative government has angered millions of Brazilians with its ambitious austerity reforms, which include the planned raising of the retirement age to fix the country's unaffordable pension system.
Temer says the reforms are already helping to end a two- year recession, but with 13.7 per cent unemployment, many Brazilians do not feel the supposed improvements.
Yesterday, thousands of people demonstrated against Temer in the capital Brasilia and in Rio de Janeiro.
Rousseff's leftist Workers' Party planned nationwide protests on Sunday, with turnout likely proving an important barometer of the national mood.
Even a former chief justice of the Supreme Court, Joaquim Barbosa, called for Temer's head.
"There is no other way out. Brazilians must mobilise, must take to the streets to forcefully demand the immediate resignation of Michel Temer," he said on Twitter.
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