After wrapping up a historic meeting with North Korean dictator Kim Jong Un, President Trump told reporters on Tuesday he is halting the "war games" consisting of joint military exercises with South Korea. He also said he wants to bring American soldiers in the Korean Peninsula back home "at some point."

"We have right now 32,000 soldiers in South Korea. And I'd like to be able to bring them back home. But that's not part of the equation right now," Mr. Trump said.

Sen. Lindsey Graham, R-South Carolina, an Air Force veteran, balked at the idea of U.S. soldiers leaving the region.

"I don't mind putting these exercises on hold. Over the arc of time, the exercises won't matter. But the one thing I would object to violently is withdrawing our forces from South Korea," Graham said Tuesday on "CBS This Morning." "China is trying to play President Trump through North Korea. China's goal for decades has been to drive us out of Asia. If we withdraw our forces and that's part of the deal, I can't support the deal. That will lead to more conflict, not less. Our forces in South Korea are stabilizing for Asia."

CBS News senior global affairs contributor and Eurasia Group president Ian Bremmer also stressed China's role in the region, calling China "the big winner" in the historic summit.

"The most important takeaway here long term is that the United States is probably going to be a much more marginal player at the end of the day in this region," Bremmer said. He pointed to a "freeze for freeze" happening between the U.S. and North Korea to illustrate the point.

"The North Koreans are freezing their ICBM and nuclear tests, and the Americans are freezing our military exercises with the South Koreans. That is exactly the formation that the Chinese have asked for over the course of the past year, and we said absolutely not," Bremmer said.

Mr. Trump's announcement that the joint exercises would end appeared to catch some U.S. defense officials off-guard. Department of Defense spokesperson told CBS News in a statement on Tuesday, "The Department of Defense continues to work with the White House, the interagency, and our allies and partners on the way forward following the U.S./DPRK summit." As of Tuesday morning, United States Forces Korea, who conducts the exercises, said in a statement they had received "no updated guidance on execution or cessation of training exercises."

Graham, who called the "comprehensive" document Mr. Trump and Kim signed on Tuesday an "agreement in principle," said the end of the military exercises with South Korea gives the U.S. "breathing space" to get a detailed denuclearization agreement with North Korea that Congress would then have to approve.

"We're not stopping training. We're stopping joint exercises for a while to give Kim Jong Un some assurance that we're willing to meet him more than halfway," Graham said. "I am willing to do a lot of things to get them to give up their nuclear weapons and end their missile program. I'm – you know, he can have a membership at Trump National [golf course] – I really don't care how generous we are as long as we don't go too far when it comes to our troop presence."

"At the end of the day, this is the last, best chance to end this conflict without a war," Graham added. "I'm very open-minded to security agreements and to economic incentives to North Korea. But I am very closed minded when it comes to withdrawing our forces."