Ms. Rousseff, like Mr. Temer, is also deeply unpopular. But as she strays from the spotlight, Mr. Temer is receiving greater scrutiny over testimony tying him to illegal campaign financing operations.

Executives at the construction giant Odebrecht told investigators that Mr. Temer had requested more than $3 million for his centrist Brazilian Democratic Movement Party. As part of a plea deal they are seeking, the Odebrecht executives said the payment had been made in cash through a unit used to deliver bribes, according to Veja, a newsmagazine.

Mr. Temer has already been found guilty of violating campaign finance limits, a conviction that could make him ineligible to run for office for five years. In a statement, Mr. Temer’s media office acknowledged that he had requested the funds from Odebrecht but said they had been legally declared to the electoral authorities.

Mr. Temer endured a chorus of boos when he briefly declared the start of the Olympics during the opening ceremony on Friday. Ticket holders appeared at various Olympic events over the weekend with placards reading, “Fora Temer” (Out with Temer.)