US President Donald Trump took his enthusiasm for his detente with North Korean leader Kim Jong-un to new heights on Saturday, declaring at a rally with supporters that "we fell in love" after exchanging letters.

Mr Trump and Mr Kim have said they want to work toward denuclearising the Korean peninsula, holding an unprecedented meeting earlier this year in Singapore to discuss the idea.

Before they turned the page on decades of public acrimony, the leaders regularly traded threats and insults as North Korea pushed to develop a nuclear missile capable of hitting the United States.

"I was really being tough - and so was he. And we would go back and forth," Mr Trump told a rally in West Virginia.

"And then we fell in love, okay? No, really - he wrote me beautiful letters, and they're great letters," he said.