Jude Law, reeling from rumors that he and Nicole Kidman were having an affair while shooting the movie "Cold Mountain," has fiercely spoken out on the matter.

According to Australia's Sydney Morning Herald (Kidman, 35, is Australian), Law, 30, insists that there was "absolutely no third party involved" in his marriage to actress Sadie Frost, 37. "To suggest otherwise is malicious, hurtful and libelous."

As was reported last week, Frost, 37, was admitted to a hospital last week suffering from post-natal depression following the birth of the couple's son Rudy. (She is now reported to be recovering at the couple's north London home.)

But some tabloids went on to speculate that the chief reason for her treatment was her handsome husband's alleged relationship with the ex-Mrs. Tom Cruise.

In a statement Monday night through his American publicist, Law said: "I have been on to my lawyers and will follow all legal action necessary to ensure that these kind of vicious lies are put to a stop."

He explained, "My family and I are angry and saddened by the malicious, mean-spirited and absolutely untrue stories that have run in the press over the past two weeks.

"Other than the fact that my wife has been suffering from post-natal depression -- for which she has been receiving treatment -- there is not one shred of truth in anything that has been written. "

He emphasized, "There is absolutely no third party involved in our marriage."

Meanwhile, speaking of unsubstantiated press reports, Dennis Quaid's publicist told PEOPLE.com on Monday that the "Far From Heaven" actor, 48, "is not engaged" to be married, despite a story in British tabloid the Sun reporting that former sales girl Anna Poche, 20, showed her hairdresser photos of Dennis and said, "This is my fiance -- isn't he cute?"