BOSTON—The parents of the Boston Marathon bombing’s youngest victim are urging federal prosecutors in a new statement to stop seeking the death penalty for Dzhokhar Tsarnaev to avoid years of appeals that would keep the attacks in the public eye.

“We are in favor of and would support the Department of Justice in taking the death penalty off the table in exchange for the defendant spending the rest of his life in prison without any possibility of release and waiving all of his rights to appeal,” wrote Denise and Bill Richard,...