"I fully understand that Danish veterans have said no words can describe how much this hurts," she said on Facebook.
"It is unacceptable that the American president questions the commitment of allied soldiers in Afghanistan," she added.
The Danish Veterans Association earlier said it was "at a loss for words".
"Denmark has always stood by the United States, and we have shown up in crisis zones around the world when the United States asked us to," the association said in a statement.
Danish veterans are calling for a silent march in Copenhagen on January 31 to protest Trump's remarks.
"Denmark is one of the NATO countries that has suffered the highest losses per capita," the Danish prime minister underscored.
Denmark's population was about 5.4 million in 2003 and, according to the Danish news agency Ritzau, around 12,000 Danish soldiers and civilians have been sent to Afghanistan over the years.
"My thoughts are with the veterans, your families, and your loved ones, who in no way deserved this," she added.
In an interview with Fox News aired on Thursday Trump said NATO will "say they sent some troops to Afghanistan.
"And they did, they stayed a little back, a little off the front lines," he added, triggering outrage in Britain, which lost 457 soldiers during the NATO mission in Afghanistan.
Soldiers from Canada, France, Germany, Italy, Denmark and others also died in the conflict.
British Prime Minister Keir Starmer said Friday: "I consider President Trump's remarks to be insulting and frankly, appalling, and I'm not surprised they've caused such hurt to the loved ones of those who were killed or injured."
The White House rejected Starmer's comments and defended Trump.
"President Trump is absolutely right -- the United States of America has done more for NATO than any other country in the alliance has done combined," Taylor Rogers, a White House spokeswoman, said in a statement sent to AFP.
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