Sturgeon said she is sure "the president has policy disagreements with me," as he will with many other governments.
But "as first minister of Scotland, I'm not going to decline to meet president Trump," she said.
"What I'm very keen to stress is that regardless of who occupies the office of president or first minister at any given time, the relationship between Scotland and the United States is a strong one," Sturgeon said. "It's very longstanding. It spans family, culture, business, and part of our purpose here in the United States is to strengthen, to build on that relationship."
That relationship, she said, is "more important than any transient policy disagreements between the governments of the two countries."
A strong advocate for gender equality, Sturgeon spoke at a United Nations meeting earlier Wednesday on human rights and the role of women in building peace. She reportedly backed Democratic candidate Hillary Clinton in the election and has had no meetings with Trump or his administration during her trip, which she said has focused mainly on strengthening trade and U.S. investment in Scotland.
According to U.S. census figures, there are 10 million Americans with Scots or Scots-Irish ancestry, Sturgeon said, "but surveys repeatedly show that there are around 30 million people in America who claim to have Scots ancestry."
"That says to me there are 20 million people who are not Scottish in America but would like to be Scottish. So that's a massive opportunity for us to build on," she said.
Sturgeon said there has also been enormous interest in the United States on the United Kingdom's decision last year to leave the European Union and the Scottish Parliament's vote on March 28 authorizing her to ask the British government for a new referendum on independence.
Scotland voted to remain in the EU in last year's Brexit referendum and Sturgeon said it should have "the right to look at its future" and have the choice of whether to remain part of the United Kingdom or become independent.
Sturgeon is pressing for a referendum between the fall of 2018 and spring of 2019, before Britain leaves the European Union but when details of the divorce are clear. British Prime Minister Theresa May, who is battling to hold the United Kingdom together, has made clear, however, that it isn't time for another vote.
Scottish voters rejected independence in a 2014 referendum that Sturgeon's Scottish National Party called a once-in-a-generation vote. But Sturgeon says Brexit has altered conditions dramatically.
"I'm very confident that Scotland will be an independent country in my lifetime — well within my lifetime — and take its seat at the United Nations alongside all the other independent countries of the world, large and small," the 46-year-old Scottish leader said.
Sturgeon said a new referendum "should be on the same basis as the last referendum."
She called prime minister May's position "not a sustainable one."
Sturgeon said she put forward compromises "but we haven't had any sign from the UK government that they want to meet us half way."
"Simply saying now is not the time only takes you so far before you have to answer the question, well when is the time?," she said. "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. I'll set out in due course the steps I intend to take next."
Sturgeon said she would want an independent Scotland to definitely seek membership in the European Union and also "continue to cooperate with our family across the British isles."
"Scotland and England should always trade freely with each other," Sturgeon said. "It's in our mutual benefit. But I want that as well as trade within the single market because that is so important to Scotland's interests."