Ivanka, a senior adviser to the president, was questioned last month by Chelsea's former employer, NBC News, about sexual misconduct allegations leveled against her father.
The friendship between Chelsea Clinton and Ivanka Trump has apparently cooled.
"I think it's a pretty inappropriate question to ask a daughter if she believes the accusers of her father when he's affirmatively stated that there's no truth to it". The commander in chief's eldest daughter said previous year that liberal critics have "unrealistic expectations" of her ability to influence her father's agenda.
The daughter of two of the biggest names in American politics, Chelsea Clinton developed into an accomplished young woman of her own, both in academics and the arts.
It has been over a year since Donald Trump was inaugurated as the 45th President of the United States, marking the end of what was undoubtedly the meanest presidential election of all time, pitting the once friendly Trump and Clinton families against each other.
Host Sunny Hostin said the question was "completely fair game" because she works at the White House, and her "platform is supposed to be about helping women".
These women have accused Bill Clinton of rape or sexual assault
Chelsea then dug in further, saying: "I think, unfortunately, this administration is the collision of cruelty and incompetence".
Colbert jokingly asked: "Could you call her up and say, 'Hey, maybe no war with North Korea?'"
"Problem is, we don't have Stars anymore - except your President (just kidding, of course)", Trump tweeted.
Chelsea said anyone working for the president "should expect to be scrutinized for whatever decisions, not only he or she is making, but whatever decisions the White House is making on any given day".
'It's none of your business, ' Chelsea Clinton said at the time.
She continued, "Whatever issue you care about, please, like, lead us forward on that". We've stayed close to one another, maybe a little less publicly so, but she's a good friend.