HANOI, Vietnam — It was an unlikely bromance that began last summer in Singapore. The relationship seemed ready to blossom even more this week in Vietnam — until, suddenly, the date went sour.

President Trump, who prides himself on his negotiating skills, began his second summit meeting with Kim Jong-un — the North Korean dictator who is believed to have ordered the killings of both his own uncle and half brother — with ardent wooing.

“I think very importantly, the relationship is, you know, just very strong,” Mr. Trump said on Thursday morning as he sat with Mr. Kim before a phalanx of cameras at the Metropole Hotel in Hanoi, the Vietnamese capital. “And when you have a good relationship, a lot of good things happen.”

Mr. Kim, for his part, was equally gushing as he said that “nearly all of the world” was watching and was “probably thinking that they are seeing a scene from a fantasy movie now that they are seeing us spending wonderful time together facing each other.”