Set against a tense, eerie silence in the landmine-riddled mountains separating South and North Korea, the Demilitarized Zone may be the highest-stakes negotiation site on earth. It’s not the sort of place for mistakes.

It is the latest spot where Ivanka Trump has tried her hand at statecraft.

On Sunday, Ms. Trump, the president’s elder daughter, used an impromptu meeting between her father and Kim Jong-un, the North Korean leader, to further slip into the role of unofficial spokeswoman and budding stateswoman for the Trump administration. With her husband, fellow senior adviser Jared Kushner, at her side, Ms. Trump delivered news interviews, posed for photos and met Mr. Kim.

Earlier in the day, Ms. Trump had repeated what her father has often said about dealing with the North: that it would be free of crippling sanctions and clear for an economic boom if Mr. Kim were to dismantle his nuclear program. Scant evidence suggests that Mr. Kim is taking the steps to do this, but on Sunday, two Trumps rewarded him with a visit.

“We are on the precipice of ushering in potentially a golden era for the Korean Peninsula,” Ms. Trump told Bloomberg News in the hours before her father took the historic step of crossing into the North. But by the time she emerged from a building designed for negotiations hours later, she only had one word for journalists about her encounter with North Korea.