The Scottish First Minister is now on a week-long tour of America but has not arranged to meet any members of the President's administration.
"In order to advance women's rights, we need to make sure that women are in key areas and key positions of influence", she said.
Mr Trump has often celebrated his Scottish ancestry, as his mother came from the Western Isles.
In response to a challenging question about whether her search for Scottish independence conflicted with the values of the United Nations, she responded: "One of the reasons I want us to be self-governing is precisely because I want us to play a constructive and better role in the wider world".
But she also said she strongly believes it's important "to stand up and champion values that we hold dear and not allow a diplomatic silence to get in the way of doing that".
During a tour of the USA in which she has not met the president's team, she said that she does not object to the golf courses in Ayshire and Aberdeenshire owned by Mr Trump's corporation and welcomes the U.S. investment they bring.
Speaking about the Scotland Act - which sets out what powers are devolved to the Scottish parliament - Sturgeon said: "One of the things it reserved to the United Kingdom government is the constitution, which is quite a vague term".
Scottish voters rejected independence in a 2014 referendum that Sturgeon's Scottish National Party called a once-in-a-generation vote.
US stocks off to a mixed start Thursday
While both beers appeal to a wide swath of demographics, Latino drinkers remain important to the Mexican beer business. Total sales for the quarter came in US$1.63bn, slightly ahead of the US$1.59bn Wall Street analysts had forecast.
Driver using phone hits cop enforcing distracted-driving law
Texting and driving requires motorists to take their eyes off the road, hands off the wheel, and mind off the task of driving. The national campaign slogan is "You Drive, You Text, You Pay", but it's not all about texting. "But we want to be clear".
Maricopa County Sheriff announces shutdown of Tent City, Joe Arpaio's infamous jail
Last November, voters in Maricopa County, Arizona, finally ousted "America's Toughest Sheriff" Joe Arpaio from office. One tradition started by Arpaio, making inmates wear pink underwear, has already been slowly phased out.
Last year, 50 women took part in the Scottish programme and the same number will take part in the initiative every year until 2021, said Sturgeon.
A joint agreement committing the Scottish Government and the state of California to work together to tackle climate change has been signed. "I might put forward the timescale I think makes sense, and if she doesn't agree with that then we should discuss what the alternative might be".
"It is good to see climate action high on the agenda of Scotland's first minister on her trip to the United States", Lou Leonard, WWF-US's senior vice president for climate change and energy, said in a statement.
Sturgeon said she has no objection to the golf courses and welcomes US investment. "It's in our mutual benefit".
That relationship, she said, is "more important than any transient policy disagreements between the governments of the two countries". "When Nicola Sturgeon is overseas she should be representing the interests of all the people of Scotland, not trying to build up support for a second referendum that the majority here don't want".
Ms Sturgeon was speaking ahead of an address at the United Nations in NY on the subject of human rights and the role of women in peacekeeping around the world.
Be proactive - Use the "Flag as Inappropriate" link at the upper right corner of each comment to let us know of abusive posts.