Scotland’s First Minister also stressed the importance of championing values after she told media she would be willing to meet the billionaire tycoon who she has strongly criticised in the past.
Mr Trump has often celebrated his Scottish ancestry, as his mother came from the Western Isles.
Ms Sturgeon, however, revoked his status as business ambassador for Scotland after he proposed banning Muslims from entering the US in 2015.
In an interview with the Associated Press on Wednesday, she said: “The fact that Donald Trump owns golf courses in Scotland does not mean that if I disagree with him on a matter of policy or a matter of principle that I will not say that.
“But I would seek to operate in a way that is respectful and constructive.”
Ms Sturgeon stressed how important it is “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 US 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 US investment they bring.
Earlier Ms Sturgeon said she fully expected Mr Trump to visit Scotland and that she was “not going to decline to meet him”.