The danger is immediate: North Korea has fired missiles over Japanese territory, while China is confronting the prospect of war on its border.
Trump warned last year that further provocations from Pyongyang would be met with "fire and fury like the world has never seen." In August, after Kim had declared that a nuclear strike launch button was ready at all times, Trump tweeted: "I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"
Against that menacing backdrop, Asian leaders see the prospect of a Trump-Kim summit as a helpful, de-escalating step, experts said. But the uncertainty surrounding the planned meeting has also created new anxieties.
Among them are that Trump was too quick to agree to a meeting without any apparent conditions, and that his sometimes impetuous approach could lead to unfortunate concessions.
"The leaders of Japan and China see significant promise but also a certain risk in the prospect of a [US-North Korea] summit," said Daniel Russel, a regional expert at the Asia Society who until last year served as assistant secretary of state for East Asia.
"For both Abe and Xi Jinping, the rhetoric of bloody nose and fire and fury was quite concerning," Russel said. "I'm sure [the summit prospect] comes as a relief to a certain degree. But the leaders must have each wondered why they hadn't been informed in advance and - certainly in the case of our close ally Japan - why there had been no prior consultation before the US announcement."
In comments to reporters after learning of the proposed Trump-Kim meeting, Abe said the United States, Japan and South Korea should "continue imposing the utmost pressure until North Korea takes specific actions toward thorough, verifiable and irreversible denuclearisation."
Abe is expected to visit Trump in Washington next month before any meeting with Kim.
Trump lashed out at the media for failing to give him adequate credit for what he depicted as a breakthrough with North Korea, saying on Twitter that "after hearing that North Korea's leader wanted to meet with me to talk denuclearisation and that missile launches will end, the press was startled & amazed. . . . But by the following morning the news became FAKE. They said so what, who cares!"