Sturgeon told the regional Scottish Parliament on Thursday that she was not prepared to stay silent in the face of "attitudes of racism, sexism, misogyny or intolerance".
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Trump was once a business ambassador for Scotland: his mother was born on the remote northwestern Isle of Lewis and he has golf courses at either end of the country.
He was feted by Sturgeon's predecessor Alex Salmond but the two then fell out when Trump sought to block a wind farm development near his Aberdeenshire golf course.
The left-wing Scottish National Party's feud with the Republican continued under Sturgeon, who rescinded Trump's "Global Scot" status after he pledged to halt Muslim immigration into the United States.
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One Scottish lawmaker questioned whether Scotland's business links with the United States are now under threat following Sturgeon's outspoken attacks on the president-elect.
Sturgeon said it was ironic that Trump -- who has threatened to build a wall on the Mexican border -- was elected on the anniversary of the fall of the Berlin Wall 27 years ago.
She hailed German Chancellor Angela Merkel's approach to the incoming US administration.
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Sturgeon said, "Angela Merkel said that she wanted to have a constructive engagement with the new president but one based on the values of respect for all, tolerance and diversity. I echo that sentiment.
"I very much hope that we see a president Trump who is very different from the candidate Trump." She added, "The relationship between the United States and Scotland is a long-standing one and is based on ties of family, culture and business.
"I want those ties not just to continue but to be enhanced and to get even stronger." Sturgeon said Democratic candidate Hillary Clinton's defeat was a setback for gender equality.
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