The actor, who once dated Shakira, was set to front Sunday's (13Jun10) Puerto Rican Day Parade after organisers announced him as the recipient of this year's (10) International Godfather honour.
His inclusion in the street carnival sparked outrage from officials and citizens in Puerto Rico, who claimed he should not receive the award because of a domestic violence conviction which landed him in jail six years ago.
And now Rios has decided not to join the parade.
In a statement, he says, "After discussing this issue with my wife, my children and Congresswoman Nydia Velazquez, to whom I'm grateful for her wise words, my family and I have decided... not to attend the parade and promote the unity and the consensus between the Puerto Rican people at such a great event.
"Though we accept the honour... we understand the event should be one of unity, not of discord."
Rios spent three months in a Puerto Rican prison for hitting his then-girlfriend Daisy Annette Santiago.