"This includes suspending FREEDOM GUARDIAN along with two Korean Marine Exchange Program training exercises scheduled to occur in the next three months," the Defense Department said.
It added that additional decisions will depend upon North Korea "continuing to have productive negotiations in good faith."
Earlier this week, the Pentagon announced that it had suspended planning for the large-scale Freedom Guardian exercise originally scheduled for August.
Following the Kim-Trump meeting on June 12, the US president announced that he would cancel what he called "very provocative" and expensive military exercises that the United States regularly holds with South Korea.
North Korea has long lashed out at the joint military exercises.
Kim & Trump: A big deal?
At the summit, Trump and Kim pledged "to work towards complete denuclearization of the Korean Peninsula."
The vague wording left out details of how North Korea would dismantle its nuclear weapons program in exchange for sanctions relief and security guarantees.
No threat from North Korea or an extraordinary threat?
A presidential declaration sent to US lawmakers on Friday called for continuing sanctions on North Korea for another year, calling the country "an unusual and extraordinary threat."
"The existence and risk of proliferation of weapons-usable fissile material on the Korean Peninsula and the actions and policies of the Government of North Korea continue to pose an unusual and extraordinary threat to the national security, foreign policy, and economy of the United States," the declaration said.
Though the notice is considered pro forma and was expected, it was a break from earlier statements from the president, including a tweet directly following the summit saying, "There is no longer a Nuclear Threat with North Korea."
Russia, South Korea meet
Also on Friday, Russian President Vladimir Putin and South Korean President Moon Jae-in met in Moscow and agreed to "continue joint efforts to establish complete denuclearization on the Korean peninsula."