"Scotland wants to play a part," Sturgeon told diplomats at UN headquarters in New York.
"We are a relatively small country, but a country that potentially can have a big, positive and powerful voice," she said.
The head of the government is on a US tour to make the case for Scottish independence as she pushes for a second referendum on breaking away from Britain.
The Scottish government last week asked British Prime Minister Theresa May for a second referendum on independence after Britain launched the process of leaving the European Union.
The address at the United Nations was aimed at raising Sturgeon's international profile and drawing attention to Scotland's credentials as a "good global citizen."
The first minister said she wanted to "explore ways in which the Scottish government can further support the UN and its various different forums," in particular in the area of human rights and gender equality.
Scotland is working with the United Nations to offer training to women in Iraq, Syria, Yemen and other conflict areas in the Middle East to help them play a larger role in promoting peace.
Last year, 50 women took part in the Scottish program and the same number will take part in the initiative every year until 2021, said Sturgeon.
"My country will take a lead in trying to drive forward progress both within Scotland, but also where possible by helping to promote gender equality," she said.
"Women's rights have to be the concern of everybody, not just women."
"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.
Earlier this week, Sturgeon spoke to US investors in California. She is scheduled to address the Women in the World summit in New York on Thursday.