Washington (CNN) President Donald Trump's announcement that the US will stop military exercises with South Korea startled Tokyo and Seoul, unsettled US lawmakers, and took at least some parts of the Pentagon by surprise.

The declaration -- one that goes to the heart of the security of US allies and the United States' western defense perimeter -- raised concerns that Trump had made a significant concession at his summit with North Korean leader Kim Jong Un without getting anything solid in return, particularly as he raised the prospect of pulling troops out of South Korea altogether.

"It's really breathtaking," said Michael J. Green, senior vice president for Asia and Japan chair at the Center for Strategic and International Studies.

"When the President of the United States announces unilaterally to the leader of North Korea that we are going to stop our military exercises with our allies, Japan and Korea, and does not first tell those allies ... and then goes on to say that someday he'd like to get our troops out of Asia," Green said, "that's an astonishing development."

'It's inappropriate'

Many praised Trump for pursuing dialogue over confrontation . But Trump's move on military exercises reinforced concerns about his commitment to longstanding US alliances, particularly because he was offering a goal long sought by both Pyongyang and Beijing without consulting South Korea or Japan.

Others said that in giving away a significant chip so early in the game, Trump was undermining his negotiators' leverage.

And while North Korea has made a show of scaling back some of its nuclear activities, Pyongyang continues its disruptive behavior in the cyber realm and remains one of the world's most egregious human rights violators, starving its own people.

Trump made the announcement in the course of a press conference in Singapore. "It's inappropriate to be having war games," he said, calling them "provocative," an adjective North Korea might use, and adding that "it really is something that I think they very much appreciate."

"We have, right now, 32,000 soldiers in South Korea, and I'd like to be able to bring them back home," Trump said, adding that such a move isn't part of the equation right now.

Former Vice President Joe Biden echoed much of the criticism when he issued a statement saying that "the Trump administration has given the North Korean regime many sought-after wins up front without getting anything in return."

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Biden listed the "legitimacy of a meeting with the American president," the easing of the international sanctions pressure "and the suspension of our military readiness exercises," saying the move has "reduced our leverage and signaled a weakening of our alliance in return for vague promises to begin nuclear negotiations."

Green, the Asia expert at CSIS, said it was possible that the Pentagon could amend the President's statement and say, "what the President meant was we're not going to have heavy bombers in our exercises, or we're not going to escalate them because we're under a diplomatic process right now... But we've not had a president talk about pulling the troops home in over half a century."

A former State Department official characterized the announcement as "a step that can be easily reversed."

"It's not a positive sign, but (it's) also not a fatal flaw," said Thomas Countryman, a former assistant secretary of state for international security and nonproliferation, who added that he was concerned about the lack of coordination with South Korea.

"The entire process can only succeed if the United States and South Korea stay in the closest possible consultation," Countryman said during a call organized by the Arms Control Association.

South Korea's Ministry of Defense put out a statement after Trump's press conference saying it needed "to figure out President Trump's accurate meaning and intention."

There was also some question as to whether the US military was completely aware of Trump's decision. Several lawmakers, including Sen. Bob Corker, the Tennessee Republican who chairs the Foreign Relations Committee, said military leaders were in the dark.

One US defense official told CNN that they had "received no updated guidance on execution or cessation of training exercises," including the next big one in late August, called Ulchi Freedom Guardian, and would continue their current coordination and work with South Korea until told otherwise.

But Pentagon spokeswoman Dana White said Secretary of Defense James Mattis "was not surprised. He was consulted."

She noted that "conversations have been robust," and while she didn't say that Mattis supported the President's decision on exercises, she said that Mattis "is in full alignment with the President to meet his goal, which is denuclearization of the Peninsula."

.@VP was very clear: regular readiness training and training exchanges will continue. https://t.co/9tnKhqxnMz — Cory Gardner (@SenCoryGardner) June 12, 2018

A second senior US defense official said the Pentagon will now work with the White House and State Department to determine how to carry out the President's intent on exercises.

The official said the issues to be determined right now include: whether this is a temporary or permanent suspension; the level of exercises impacted -- all of them or just major ones; the impact on allies who are part of the program and whether there are any conditions North Korea must meet before exercises are called off.

Korea experts say the exercises are crucial.

"We need to have a high state of readiness to deter North Korea or, god forbid, defend South Korea," Gordon Chang, a North Korea expert, told CNN. "If you don't have those exercises, readiness erodes very quickly, working together, getting that interoperability correct."

In addition, Chang added, "That's our western defense perimeter... we need to have it strong, we need to have it whole."

Confusion reigned Monday about what Trump had actually meant when Republican lawmakers said Vice President Mike Pence had told them that military exercises would continue, a claim Pence's office immediately rebutted with his spokeswoman Alyssa Farah tweeting "@VP‬⁩ didn't say this."

Sen. Cory Gardner, a Colorado Republican who sits on the Senate Foreign Relations Committee, later tweeted that Pence said "while this readiness training and exchanges will occur, war games will not."

The announcement had already generated enough concern that lawmakers from both sides of the aisle were already talking Tuesday about steps they could take to prevent the administration from making changes to US military capability on the Korean peninsula.

"We certainly are involved in terms of the funding of our military capability in the Korean peninsula and the area," Democratic Arizona Rep. Ruben Gallego, a veteran who serves on the House Armed Services Committee, told CNN. "Any efforts that we feel in terms of changing troop levels would certainly be our purview and we would look at it very, very closely to make sure that whatever is done is in the best interest of the United States and our allies."

'No.'

Republicans echoed the sentiment , rejecting the idea of a troop withdrawal and expressing hesitation about an end to military exercises.

Sen. Roy Blunt of Missouri, a member of Senate GOP leadership, said, "I'd be concerned about any discussion of removing troops from Korea. And I will look closely at what the discussion was about our joint operations -- our joint military operations."

Republican Sen. Joni Ernst of Iowa was definitive when asked about the idea of moving American troops off of the Korean Peninsula. "No," she said. "No moving them."

Gardner said, "I think it's important that we continue to engage in South Korea as we have been, from an exercise standpoint."

At least one Republican said it would be all right to stop military exercises. Sen. Lindsey Graham of South Carolina said he was "fine" putting war games on hold, but drew the line at troop withdrawal. "One thing I cannot entertain is withdrawing our troops as part of the deal," he said.