A day after their historic summit, Donald Trump and Kim Jong-un returned to their respective strongholds Wednesday — but to far different receptions.

In Pyongyang, the North Korean autocrat woke up to state media's enthusiastic claims of a victorious meeting with the U.S. president; photos of him standing side-by-side with Trump on the world stage were splashed across newspapers. Trump, meanwhile, faced questions about whether he gave away too much in return for far too little when he bestowed a new legitimacy on Kim's rule and agreed, at Pyongyang's request, to end war games with Seoul that the allies had long portrayed as crucial to Asian safety.

Dubbing it the start of a new relationship between their countries, which are still technically at war, Pyongyang's first reports Wednesday stressed to the North Korean people that Trump agreed at Kim's demand to halt joint military exercises with South Korea as long as talks toward easing tensions continue and suggested that Trump also said he would lift sanctions as negotiations progressed.

"President Trump appreciated that an atmosphere of peace and stability was created on the Korean Peninsula and in the region, although distressed with the extreme danger of armed clash only a few months ago, thanks to the proactive peace-loving measures taken by the respected Supreme Leader from the outset of this year," said a summary of the leaders' summit by the North's state-run Korean Central News Agency.

As Trump acknowledged that denuclearization would not be accomplished overnight, the North suggested Wednesday that Trump had moved away from his demand for complete denuclearization before U.S. sanctions on the long-isolated country are removed.

"Kim Jong-un and Trump had the shared recognition to the effect that it is important to abide by the principle of step-by-step and simultaneous action in achieving peace, stability and denuclearization of the Korean Peninsula," KCNA reported.

U.S. Secretary of State Mike Pompeo, left, and White House Chief of Staff John Kelly watch a video President Donald Trump presented to North Korea's leader Kim Jong-un in Singapore on Tuesday. Pompeo has stayed behind in Asia to follow-up on the summit with briefings with allies. (Jonathan Ernst/Reuters)

Interestingly, the North made no secret of China's behind-the-scenes presence at the summit. A flurry of media coverage the day Kim arrived in Singapore showed him waving from the door of the specially chartered Air China flight that brought him from Pyongyang.

The rest of Asia was still trying to process the whirlwind events of the day before.

South official thinks drills not yet done

There was, at times, a surreal quality to the carefully staged, five-hour meeting of two men who'd been threatening each other with nuclear war and insulting each other's mental and physical attributes just months before. Trump repeatedly praised Kim's negotiating skills and their new relationship and expressed hope for "a bright new future" for Kim's impoverished nation.

But there were worries, especially in Tokyo and Seoul, which both have huge U.S. military presences, about Trump agreeing to halt U.S. military exercises with South Korea, which the North has long claimed were invasion preparations. That concession to Kim appeared to catch the Pentagon and officials in Seoul off guard, and some South Koreans were alarmed.

"The United States is our ally, so the joint military drills are still necessary to maintain our relationship with the U.S.," said Lee Jae Sung, from Incheon. "I think they will be continued for a while."

U.S. Secretary of State Mike Pompeo left Singapore on Wednesday on his way to Seoul, where he planned to meet privately in the evening with Gen. Vincent Brooks, commander of U.S. Forces Korea.

Pompeo will meet President Moon Jae-in on Thursday morning to discuss the summit. Japanese Foreign Minister Taro Kono is also heading to Seoul and is due to meet with Pompeo and his South Korean counterpart. Pompeo, the former CIA director, then plans to fly to Beijing to update the Chinese government on the talks.

On the issue the world has been most fixated on — North Korea's pursuit of a nuclear arsenal meant to target the entire U.S. mainland — Trump and Kim signed a joint statement that contained a repeat of past vows to work toward a denuclearized Korean Peninsula. The details of how and when the North would denuclearize appear yet to be determined, as are the nature of the unspecified "protections" Trump is pledging to Kim and his government.

Despite the confusion and disappointment among some, the summit managed to, for a time at least, reset a relationship that has long been characterized by bloodshed and threats. In agreeing to the summit, Trump risked granting Kim his long-sought recognition on the world stage in hopes of ending the North's nuclear program.

Verification process unknown

North Korea is believed to possess more than 50 nuclear warheads, with its atomic program spread across more than 100 sites constructed over decades to evade international inspections. Trump insisted that strong verification of denuclearization would be included in a final agreement, saying it was a detail his team would begin sorting out with the North Koreans next week.

Moon has championed engagement with the North, and the agreement's language on North Korea's nuclear program was similar to what the leaders of North and South Korea came up with at their own summit in April. Trump and Kim referred back to the so-called Panmunjom Declaration, which contained a weak commitment to denuclearization but no specifics on how to achieve it.

The Singapore agreement does not detail plans for North Korea to demolish a missile engine testing site, a concession Trump said he'd won, or Trump's promise to end military exercises in the South while negotiations between the U.S. and the North continue. Trump cast that decision as a cost-saving measure, but also called the exercises "inappropriate" while talks continue.

U.S. President Donald Trump, right, and North Korea's leader Kim Jong-un meet at the start of their summit at the Capella Hotel on the resort island of Sentosa, Singapore on Tuesday. (Jonathan Ernst/Reuters)

While progress on the nuclear question was murky, the leaders spent the public portions of their five hours together expressing optimism and making a show of their new relationship. Trump declared he and Kim had developed "a very special bond," and seemed to delight in giving Kim a glimpse of the presidential limousine. Kim, for his part, said the leaders had "decided to leave the past behind" and promised, "The world will see a major change."

The U.S. has stationed combat troops in South Korea since the end of the Korean War in the 1950s and has used them in a variety of drills. The next scheduled major exercise, involving tens of thousands of troops, normally is held in August.

The Pentagon said Tuesday it was consulting with the White House and others, but was silent on whether the August exercise would proceed. Mattis's chief spokeswoman, Dana W. White, told reporters he was "in full alignment" with Trump.

In Japan, the prospect of cancelled U.S.-South Korean drills was met with concern.

"The U.S.-South Korea joint exercises and U.S. forces in South Korea play significant roles for the security in East Asia," Japanese Defence Minister Itsunori Onodera told reporters Wednesday. He said he planned to continue sharing the view with Washington and Seoul.

In South Korea, the liberal Kyunghyang Shinmun newspaper said Trump and Kim have started a "march of peace" to end nearly seven decades of hostility and pave the way for permanent peace and prosperity on the peninsula.

The conservative Chosun Ilbo, the country's biggest paper, was decidedly more critical, denouncing Trump for offering the end of military drills while failing to convince the North to commit to verifiably giving up its nukes for good. It called the summit "dumbfounding and nonsensical," and said it will allow North Korea to permanently maintain its nuclear weapons program.