"It's impossible to resign. I'm not going to resign because I have nothing to do with this," he told a press conference at CBF headquarters in Rio de Janeiro.
He said it made him "sad" to see Marin arrested Wednesday along with six other top football officials on US charges of taking millions in bribes.
"It makes you very angry, perplexed because of everything that happened. But we have to look beyond friendship and do our job," he said.
Del Nero flew home today morning from Switzerland, where he had been due to take part in FIFA's elections to choose the president of the world football governing body.
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He said on arrival he wanted to "clarify" the situation after Swiss police arrested Marin and the other officials in a dawn raid on their Zurich luxury hotel.
Marin, 83, was CBF president from 2012 to 2015, and is a current member of the FIFA organizing committee for the Olympic football tournaments.
Del Nero, who was a CBF vice president under Marin, succeeded him last month, when Marin stepped down and became a vice president.