WASHINGTON — While the two Koreas were gingerly reopening a border hotline, President Trump was gleefully taunting Kim Jong-un about the relative size of their nuclear launch buttons.

That, in a nutshell, captured the challenge facing the Trump administration as South Korea embarked on fragile new talks with North Korea on Wednesday.

The United States, the South’s key ally, views the overture with deep suspicion. For months, it has said that talks with North Korea would make no sense until its leader, Mr. Kim, at least curbs his provocative behavior, or at best agrees to relinquish his nuclear arsenal. Mr. Trump recently has talked about the potential for war, not a diplomatic breakthrough.

Yet the president, so accustomed to being the center of attention, must now watch from the sidelines as these longstanding enemies open a dialogue. The talks at first are likely to focus on North Korea’s potential participation in the Winter Olympics, which are being held next month in the South Korean city of Pyeongchang.