In an interview with ABC News, she said, "I'm a mother and a first lady, and I have much more important things to think about and to do."
"It is not concern and focus of mine," she added in the clip released Friday.
She also noted that she thinks there are people in the White House who she doesn't trust and who may not have the president's best interest in mind.
"I know people like to speculate and media like to speculate about our marriage," she said in a taped interview last week during her first solo foreign trip.
When asked if she's been hurt by the allegations, she paused and said, "It's not always pleasant, of course, but I know what is right and what is wrong and what is true or not true."
Asked if she and the president still have a good marriage and if she still loves him, she replied, "Yes, we are fine."
"It's what media speculate, and it's gossip. It's not always correct stuff," she said.
She later added, "I'm very strong, and I know what my priorities are."
Previously, Trump has avoided publicly addressing the allegations of the President's infidelities during their 13-year marriage.
Earlier this year, accusations of his infidelity came into focus when adult film actress Stormy Daniels claimed to have had an affair with him more than a decade ago. Her assertion came in an attempt to void a nondisclosure agreement she signed just weeks before the 2016 presidential election. In doing so, Daniels also put a spotlight on the $130,000 hush money payment from the president's lawyer at the time, Michael Cohen.
President Trump has admitted to reimbursing Cohen for the payment but continues to deny the affair itself.
The president's personal attorney, Rudy Giuliani, said in June that Trump "believes her husband, and she knows it's untrue." But in her interview with ABC News, Trump said she never discussed the matter with Giuliani.
"I never talked to Mr. Giuliani," she said. When asked why he made that claim, she responded, "I don't know. You need to ask him."0comments
A second woman, former playboy Karen McDougal, also alleged that she and President Trump carried on a 10-month affair 10 years ago. Hedenied McDougal's claim as well.
Watch the full interview when Being Melania — The First Lady airs Friday at 10 p.m. ET on ABC.