- The Shanghai composite climbed 0.9 percent in its best day since May 31.
- Japan's Nikkei 225 closed up a third of a percent at 22,878.35, after briefly touching its highest level since May 22.
- South Korea's Kospi spiked 0.38 percent to its highest level since May 29, but erased those gains to close 0.05 percent lower.
Both signed an agreement that reaffirmed "unwavering commitment to complete denuclearization of the Korean Peninsula." But the document offered few details.
The Shanghai composite climbed 0.9 percent in its best day since May 31. The index reached its highest level in two days. The Hang Seng rose 0.1 percent.
The iShares China large-cap ETF (FXI), which tracks stocks of large Chinese companies traded in Hong Kong, has climbed an average 0.9 percent in the two trading days after talks between leaders of North and South Korea that indicated improved relations, according to CNBC analysis using quantitative analytics tool Kensho. The majority of North Korea's trade is with China, which supplies most of the rogue state's oil.
The close relationship between the two also makes China an important part of U.S. efforts to put pressure on North Korea. However, trade tensions between the U.S. and China have increased in the last few months.
"President Xi [Jinping] of China ... has really closed up that border, maybe a little bit less so over the last couple of months, but that's OK," Trump said during a press conference shortly after 4 a.m. ET. Trump added he would likely call Xi "very shortly" about the summit with Kim.
Japan's Nikkei 225 closed up a third of a percent at 22,878.35, after briefly touching its highest level since May 22. The iShares MSCI Japan ETF (EWJ) was unchanged in premarket trading.
South Korea's Kospi spiked 0.38 percent to its highest level since May 29, but erased those gains to close 0.05 percent lower. The iShares MSCI South Korea Capped ETF (EWY) is down 1.5 percent this year amid uncertainty in North Korea tensions. The ETF was unchanged in premarket trading.
"We will be stopping the war games, unless and until we see that the future negotiation is not going along like it should," Trump said. "But we'll be saving a tremendous amount of money. Plus I think it's very provocative."
However, Trump said the U.S. will not reduce military capability in the region.
North Korea would like the U.S. to remove its troops from South Korea, and made threats around U.S.-South Korea annual joint military exercises.
European stocks traded little changed as of 4:58 a.m. ET. U.S. stock index futures pointed to a flat to mildly lower open.
— CNBC's Gina Francolla contributed to this report.