"Given the brevity of this marriage and the most recent and tragic loss of his mother, Johnny will not respond to any of the salacious false stories, gossip, misinformation and lies about his personal life," Depp's representative told E! News Thursday.
"Hopefully the dissolution of this short marriage will be resolved quickly."
Heard officially sought to end the marriage Monday, citing "irreconcilable differences" as the reason for the collapse of the relationship.
According to legal documents, Heard said they separated May 22, meaning the Rum Diary co-stars broke up just days after the death of Depp's mother, Betty Sue Palmer.
E! said Wednesday Heard, 30, is seeking spousal support from Depp, 52, and TMZ said they had no pre-nuptial agreement.