"I'm a mother and a first lady, and I have much more important things to think about and to do", she said."I know people like to speculate and media like to speculate about our marriage", she continued.
"It is not [a] concern and focus of mine", she stressed.
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.
The interview took place in Africa during Trump's first official solo trip to the nation.
The first lady said she doesn't know why Giuliani would make such a claim about her marriage.
In a previously released clip from the same interview, the first lady told Llamas there are people close to the president she does not trust, and she "let him know".
She went on to admit that the speculation still isn't "pleasant".
Royal rewear: Duchess Kate steps out in recycled Emilia Wickstead dress
The Cambridges have two older children - Prince George , five, and Princess Charlotte, three. The duchess first showed off the Emilia Wickstead dress on a trip to Germany previous year .
She later added, "I'm very strong, and I know what my priorities are".
Addressing their 13-year marriage, Melania commented laconically: "We are fine".
She then reiterated that the "media world is speculating". It is not always correct stuff'.
"The jacket", she replies in the snippet, which doesn't give away details.
Llamas tried to get her to tell America if she has been hurt by her husband.
Melania wore then jacket, emblazoned with the words "I really don't care", while en-route to visit child migrants held at a USA detention centre, sparking controversy.
You can catch the full interview on ABC at 10 p.m. ET Friday.
She played down a suggestion the repeated rumors of his philandering had put a strain on their marriage.