President Trump is hailing an agreement between North and South Korean leaders in their historic summit, tweeting: "KOREAN WAR TO END! The United States, and all of its GREAT people, should be very proud of what is now taking place in Korea!" On Friday, South Korean President Moon Jae-in and North Korean leader Kim Jong Un pledged to work toward denuclearizing the Korean Peninsula and declaring a formal end to the Korean War by the end of the year.

National security experts, and even the South Korean foreign minister, are crediting Mr. Trump for bringing North Korea to the table.

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North & South Korea declare new era of peace

"I think the president deserves credit for getting us this far. No president has put as much pressure on North Korea as Donald Trump has, and that's a good thing," CBS News senior national security contributor Michael Morell said Friday on "CBS This Morning." Morell spent more than three decades at the CIA, becoming the deputy and acting director. But he said the outcome of the Kim-Moon summit was "not surprising."

Michael Morell (left) and Sandy Winnefeld

"Both North Korea and South Korea desperately want the Kim-Trump summit to happen, right? And they wanted their talks to be extraordinarily positive," Morell added.

CBS News military and homeland security analyst Sandy Winnefeld, a retired Navy admiral and former vice chairman of the Joint Chiefs of Staff, said on "CBS This Morning" Mr. Trump gets "some credit."

"He's put unprecedented pressure on North Korea, both militarily and economically," Winnefeld said. "By the same token, North Korea feels they put unprecedented pressure on us by achieving the nuclear weapons capability. But I would give the president good credit for placing that pressure on the North."

Both experts agree there's a long way to go, and "the real work has yet to come," Morell said. As the Kim-Moon summit sets the stage for an expected meeting between Mr. Trump and Kim, Winnefeld said both the U.S. and North Korea "feel that they're there in a position of strength." But the countries are coming with different expectations, according to Morell, and misreading each other.

Morell: Korean summit "was all aspirations"

"North Korea's expectation is, 'We are now a nuclear-weapon state. Treat us like one. We're willing to negotiate limits to our program to get rid of the sanctions.' [The U.S. is] coming at it from the perspective of, we have strangled you with sanctions, now give up your program, and then we'll be willing to get rid of [the sanctions]," Morell said.

He also said Kim Jong Un cannot be trusted.

"The Kim regimes, so three of them now, have shown over and over again a willingness to make an agreement, and then either break that agreement or cheat on that agreement. So whatever we agree to, there's got to be a very tough verification regime," Morell said.

Winnefeld said even if there is a peace agreement on the Korean Peninsula, U.S. troops will likely stay in the region for "quite some time."

"We will probably remain on the peninsula just to be a buttress for South Korea to build their confidence that this is not a mirage, just as we have troops in Europe," Winnefeld said.