They filed a written defence to a committee in Congress tasked with drawing up a recommendation on whether he should face trial over the allegations.
Temer faces a series of hearings before lawmakers vote on whether he should face a criminal trial over claims he accepted the bribe from a meatpacking firm.
He has denied the accusation, which has made him the first sitting Brazilian president to face formal criminal charges.
"He committed no crime," said his lawyer Antonio Claudio Mariz de Oliveira after filing the written defence.
Police arrested an adviser of Temer's with a suitcase full of money, which prosecutors allege was destined for Temer as a bribe.
A video has also emerged of Temer apparently approving the payment of hush money to a jailed ally. Temer's lawyer said yesterday that video was "technically doubtful."
Former vice-president Temer took over as president last year after his leftist predecessor Dilma Rousseff was impeached on charges of budgetary wrongdoing which she branded a "coup."
Temer is trying to push through reforms to save Brazil from recession. But his time in office has been blighted by the resignations of ministers and corruption claims creeping ever closer to his door.
The charges come against the backdrop of a sweeping graft investigation which has uncovered systemic corruption in the political and business elite in Latin America's biggest country.
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