Washington (CNN) If Ivanka Trump is "complicit," as critics and even a "Saturday Night Live" perfume sketch allege, she's not concerned.

"I don't know what it means to be complicit, but I hope time will prove that I have done a good job and much more importantly, that my father's administration is the success that I know it will be," Trump told CBS News' Gayle King in an interview taped Tuesday

Asked by King how she feels about the accusation, Trump defended herself.

"I don't know that the critics who may say that of me, if they found themselves in this very unique and unprecedented situation that I am now in, would do any differently than I am doing," she said. "So I hope to make a positive impact."

The interview, taped at her Washington home, was Trump's first since her father, President Donald Trump, assumed office in January.

Since officially joining her father's administration as special assistant to the President, she has slowly ramped up her public appearances, speaking last week at an event promoting young woman in STEM and discussing apprenticeships and vocational training earlier Tuesday.

Though she initially eschewed a defined role -- she once said, "I'm going to be a daughter" in her father's White House -- Trump said her path to formally joining the administration happened "organically" during the early days of the presidency.

"I realized that having one foot in and one foot out wouldn't work," she said. "And the reality is that it all happened very organically for me."

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In her new role, Trump will continue her work on women's economic empowerment.

"I'm very focused on the role of education," she added.

The President's eldest daughter, who has been a key and trusted adviser to her father well before his bid for office, was asked how she would respond to critics holding her accountable for not speaking out against her father's positions.

"I would say not to conflate lack of public denouncement with silence. I think there are multiple ways to have your voice heard. In some cases, it's through protest and it's through going on the nightly news and talking about or denouncing every issue on which you disagree with," said Trump, who has been absent from the media circuit until this interview.

"Other times, it is quietly and directly and candidly. So where I disagree with my father, he knows it. And I express myself with total candor. Where I agree, I fully lean in and support the agenda and hope that I can be an asset to him and make a positive impact."

Rare media leaks about Trump and her husband, Jared Kushner, have crafted the pair's image as a moderating force when it comes to social issues, including LGBT rights and climate change. However, Trump declined to name an issue on which she disagrees with her father.

"For me, this isn't about promoting my viewpoints. I wasn't elected by the American people to be president. My father is going to do a tremendous job. And I want to help him do that," she said.

She also reflected on her adjustment to her life in Washington with her three small children, noting various field trips across the district, including one recent stop at a monster truck rally.

Monster Jam! A post shared by Ivanka Trump (@ivankatrump) on Feb 26, 2017 at 12:25pm PST

"They don't have them nearby in New York because I've looked for years. We went in Baltimore. But every week, I try to do something different and unique and really celebrate being in a different city and in a different community," she said.