Last year, about 50,000 South Korean and 17,500 USA troops participated in Ulchi-Freedom Guardian, billed as the world's largest command-and-control exercise and aimed at defending against a North Korean attack.
Hayden served as director of the National Security Council during the administration of President George W. Bush and as Central Intelligence Agency chief under President Barack Obama.
An end to the "war games" was not in the letter signed by the two men after negotiations ended on Tuesday.
"Kim Jong Un's agreement to meet Trump means he's having a hard time (from sanctions)".
"He's known as a hard-liner, as much as Pompeo in Washington, but both people are realists who can make a compromise if necessary", Cheong said.
"Trump expressed his intention to halt the USA -south Korea joint military exercises, which the DPRK side regards as provocation, over a period of good-will dialogue between the DPRK and the US, offer security guarantees to the DPRK and lift sanctions against it along with advance in improving the mutual relationship through dialogue and negotiation", the KCNA reported.
But Mr Trump's announcement of an end to joint war games caught South Korea by surprise.
In the face of the North's constant protest, the allies' militaries have defended the exercises as purely defensive in nature.
"So, here's the question for my Democratic colleagues: If diplomacy fails, will you support my efforts to authorize the use of military force as a last resort to convince North Korea and China things are going to be different this time", Graham said.
South Korean President Moon Jae-in on Tuesday also released a statement on the DPRK-U.S. summit, describing the joint statement as "a historic event that has helped break down the last remaining Cold War legacy on earth". In 2014, he "stormed out of the room" during military talks when the South demanded an apology for the 2010 attacks, said former South Korean military officials involved in the meeting. Now and in the months since Trump pulled out of the Iranian nuclear deal, Iranian leaders have sought to deliver one consistent message to North Korea: President Trump is an unreliable partner.
Trump has already spoken to Moon by phone, in a 20-minute call following the United States president's historic meeting with North Korean leader Kim Jong Un on Tuesday, which saw a pledge from both leaders to work towards the complete denuclearisation of the Korean peninsula.
The U.S. President and Moon held talks on the phone Monday night and are set to hold another conversation at 2020 KST, the Blue House confirmed.