Prosecutors on Thursday filed corruption charges against Eduardo Cunha, the speaker of the lower house of Congress and one of Brazil’s most powerful political figures. Investigators said that Mr. Cunha, 56, a conservative evangelical Christian radio commentator who broke from President Dilma Rousseff’s governing coalition, was involved in a money-laundering operation that was part of a graft scheme at Petrobras, the national oil company. His problems intensified in July when a consultant for a Petrobras contractor testified that Mr. Cunha had solicited and accepted a $5 million bribe. Mr. Cunha says that he is innocent and that he will remain in his post. The Supreme Court will decide whether he will stand trial.