Sturgeon, who has been a critic of Donald Trump, said she would agree to meet the USA president and try to build on the already strong relationship between Scotland and the United States.
"I don't think there is any need, nor is there any intention, to see a matter that should be settled politically end up in the courts".
But Sturgeon revoked Trump's honorary status as a business ambassador for Scotland in 2015 after he proposed a ban on Muslims entering the United States and she told the Scottish Parliament in November that she stood by that criticism.
The first minister insisted that she was not avoiding the president, even though she was highly critical of him before...
"Ultimately, I hope that it can play some part in delivering a fair and lasting peace settlement for both Syria and other areas of conflict around the world - a settlement which is shaped by women as well as men", she said. Trump has been embroiled in a long-running legal battle surrounding the construction of a wind farm near his golf resort in Aberdeen.
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".
Scottish voters rejected independence in a 2014 referendum that Sturgeon's Scottish National Party called a once-in-a-generation vote.
Sturgeon said a new referendum "should be on the same basis as the last referendum".
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Nicola Sturgeon has signed an agreement with the Government of California pledging to work together on climate change.
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.
The first minister said she wanted to "explore ways in which the Scottish government can further support the United Nations and its various different forums", in particular in the area of human rights and gender equality.
The address at the United Nations was aimed at raising Sturgeon's worldwide profile and drawing attention to Scotland's credentials as a "good global citizen".
"Scotland and England should always trade freely with each other", Sturgeon said.
Mrs Sturgeon said on Tuesday night the position of the UK Government isn't sustainable, and the notion the referendum needed Mrs May's permission "hadn't been tested in court". "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".