South Koreans cheered, Iran warned that President Trump should not be trusted and China said it may be time to discuss lifting sanctions on North Korea as Mr. Trump and North Korean leader Kim Jong-un held an unprecedented summit Tuesday in Singapore.
Around Asia and the world, many have welcomed the flurry of diplomacy in recent months between the two adversaries, after a year of mounting tension, threats and name-calling. Hopes for peace on the long-divided Korean Peninsula, however, remain tempered by the many failed attempts in the past.
"The United States and North Korea have been in a state of antagonism for more than half a century," Chinese Foreign Minister Wang Yi said. "Today, that the two countries' highest leaders can sit together and have equal talks, has important and positive meaning, and is creating a new history."
Chinese Foreign Ministry spokesman Geng Shuang later said that United Nations sanctions against North Korea could be suspended or lifted in accordance with the North's actions. "We believe the Security Council should make efforts to support the diplomatic efforts at the present time," he said.
Trump said at a post-summit news conference that he has held off from imposing additional sanctions, but that the US would remove sanctions when the North's nuclear weapons "are no longer a factor."
Iran, meanwhile, reminded Mr. Kim that Trump should not be trusted because he could nullify any nuclear deal with North Korea, just as he had pulled out of the landmark 2015 nuclear deal with Tehran.
"We are facing a man who revokes his signature while abroad," government spokesman Mohammad Bagher Nobakht, according to the semi-official Fars news agency.
South Korean President Moon Jae-in said he "could hardly sleep last night" in anticipation of the meeting and expressed hope for "complete denuclearization and peace."
Japanese Prime Minister Shinzo Abe welcomed Kim's written commitment to complete denuclearization in an agreement signed with Trump at the end of their meeting in Singapore.
New Malaysian Prime Minister Mahathir Mohamad, on a visit to Tokyo, said that "both sides must be prepared to give in certain issues if they expect to reach a good conclusion."
At a train station in Seoul, the South Korean capital, people cheered and applauded as televisions screens broadcast the Trump-Kim handshake live.
"I really, really hope for a good outcome," said Yoon Ji, a professor at Sungshin University in Seoul. "I am hoping for denuclearization and a peace agreement and also for North Korea's economy to open up."
Not everyone was optimistic. "Trump's words that the process of denuclearization on the Korean peninsula will start 'very, very soon' is more of a wish than a fact," Konstantin Kosachev, chairman of the Foreign Affairs Committee in the upper house of Russia's parliament, wrote on his Facebook page.
"The role of the international community is important here. We must take the two leaders at their word and push them further," he wrote.
Japan's largest newspaper, the Yomiuri, printed a one-page "extra" edition in both Japanese and English that was distributed free in major cities 90 minutes after the meeting began.
Passers-by outside a Tokyo train station snapped up 500 copies. They generally welcomed the meeting as a good first step but wondered if progress would be made on the fate of Japanese abducted by North Korea in the 1970s and 1980s.
"I have no idea how much the abduction issue is being taken up at the summit, but I hope it will be a good start for that issue, too," said 70-year-old retiree Tomoaki Kenmotsu.
Sakie Yokota, the mother of Japan's iconic abduction victim Megumi Yokota told Japanese public broadcaster NHK that it seemed like a "miracle" that Trump had raised the abduction issue with Kim. "I feel, we've finally come this far."
Megumi was 13 when she was kidnapped on Japan's northern coast in 1977, on her way home from school. She is one of the 17 abductees officially recognized by the Japanese government.
Mr. Abe, meanwhile, thanked Trump for raising the abduction issue with Kim and said that "Japan will deal firmly with North Korea face-to-face" to resolve it.
The hard work remains to come, said Momoko Shimada, a 20-year-old student: "After the handshake and political show will be the real action. I believe that won't be easy."
This story was reported by The Associated Press. AP writers Jung-yoon Kim in Seoul, South Korea; Mari Yamaguchi and Kaori Hitomi in Tokyo; Chris Bodeen and researcher Shanshan Wang in Beijing; Jon Gambrell in Dubai contributed to this report.