Recent TV interview adds to confusion about the first daughter, who has said so little that the influence she plans to exert from her White House role is unclear

Ivanka Trump, who months ago stated her intention to be just “a daughter” to Donald Trump, has given her first television interview since being appointed to a formal White House position as “special assistant to the president”.

The first daughter toed a difficult line, seemingly embracing the role of policy “moderator” to her father, while at the same time telling CBS’s Gayle King: “I’m still my father’s daughter.”

“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,” Trump said in the interview which aired on Wednesday.

She declined to offer any examples of issues or areas where she disagrees with her father, but asked viewers not to assume her silence – especially on social media – was equivalent to tacit agreement.

“I would say not to conflate lack of public denouncement with silence,” Trump said. “I think there are multiple ways to have your voice heard … I don’t think that it will make me a more effective advocate to constantly articulate every issue publicly where I disagree.”

Ivanka Trump: the president's moral compass or just another mouthpiece? Read more

King raised Planned Parenthood, gay rights, women’s rights and climate change as issues where some might expect the younger Trump, who has called herself “absolutely” a feminist, to more publicly break with her father’s administration.

“We’re in a very unique time where noise equals, in a lot of people’s perception, advocacy. And I fundamentally disagree with that. I do think there’s a time for public denouncement … I also think there’s a time for discussion,” Trump said. “People who criticize me for not taking to social media on every single issue, I would ask them if that would render me more effective or less effective with the people ultimately making decisions?”

It was an interesting answer from the daughter and now adviser to a president whose hallmark has been opining on social media on most issues. But it also adds to confusion surrounding her, a public figure who has said so little, that the exact influence she plans to exert from her new White House role is entirely unclear.

On climate change, for instance, Ivanka Trump has yet to offer a concrete public opinion one way or the other. She has met with former vice-president Al Gore and actor and activist Leonardo DiCaprio on the subject, both environmental activists and strong advocates for the overwhelming science of climate change, which signaled at least an openness to their ideas if nothing else. But she also has done nothing to publicly rebuke her father who has called the phenomenon a Chinese hoax, and “a bunch of bunk”.

Facebook Twitter Pinterest Ivanka Trump greets female students highlighting the study of science, technology, engineering and mathematics while touring the Smithsonian Air and Space Museum on 28 March 2017 in Washington DC. Photograph: Win McNamee/Getty Images

The idea that Trump and her husband Jared Kushner could have a moderating impact on her father’s presidency has been a popular one since his candidacy began to gain serious traction, largely on the strength of bombastic, populist far-right pronouncements. At the 2016 Republican national convention, for example, Trump told the convention body that her father would fight for “equal pay for equal work” and for paid parental leave, both at odds with the party platform and the now president’s campaign rhetoric.

But many have also been wary of Trump as something of a wolf in sheep’s clothing. A “queer dance party” of hundreds protested outside Trump’s DC home on Sunday night to demand that she offer more than just “words of support” for LGBTQ people, Werk for Peace organizer Firas Nasr told the Huffington Post.

During the CBS interview, King asked Trump about the idea that she is “complicit” in the reckless tacks her father’s administration has taken: ostensibly for knowing better but not speaking up. Saturday Night Live has lampooned the first daughter on this point with a spoof advertisement for an Ivanka-Trump branded perfume simply called: “Complicit.”

But Trump sidestepped King, answering simply: “If being complicit is wanting to be a force for good and to make a positive impact, then I’m complicit.”

During the interview Trump bucked at the notion that her growing role in her father’s administration presented the opportunity for her to grow her personal clothing and lifestyle brand from a public office. “I would argue that if I had not come to Washington DC and if I was in New York growing my business I would be doing far better than by placing the restrictions that I have placed on my team, and ensuring that any growth is done with extreme caution.”

Trump placed her business into an “independent” trust run by her brother-in-law and sister-in-law. Last week financial disclosures from the White House revealed that Trump and Kushner are retaining scores of property assets as they transition into key players in the administration, fueling concerns of conflicts of interest.