LOS ANGELES • Pop star Madonna has quashed long-standing rumours that her former husband, actor Sean Penn, abused her during their four-year marriage.

Her statement, which was obtained and published by USA Today last Friday, had been submitted in an addendum to the US$10-million (S$14.1-million) defamation lawsuit he filed in September against Empire creator Lee Daniels, after Daniels compared him with actor Terrence Howard, who admitted to hitting his former wife.

In an interview with The Hollywood Reporter in September, Daniels had defended Howard, the star of his hip-hop television series, against reports of domestic troubles, saying the actor "ain't done nothing different than Marlon Brando or Sean Penn".

Madonna denied allegations that Penn had hit her with a baseball bat in 1987 and abused her in 1989, said USA Today. She called reports on the alleged incidents "completely outrageous, malicious, reckless and false".

"While we certainly had more than one heated argument during our marriage, Sean has never struck me, tied me up or physically assaulted me," she was quoted as saying.

Madonna, 57, and Penn, 55, have been friendly in the past year, decades after their divorce in 1989.

He attended several nights of her Rebel Heart Tour, including one at Madison Square Garden, said the Daily Mail.

She later said: "Thirty years earlier, he was upset with me for wearing a costume that was too revealing. That's not a lie. After the show, he wrote me a letter and said he finally appreciates my art."