Seoul, which has tens of thousands of US troops on its soil to help protect it from its hostile northern neighbour, said the suspension would affect the large-scale Ulchi Freedom Guardian exercises slated for August.
"South Korea and the US plan to continue discussions for further measures," the defence ministry said in a statement, adding that "no decisions have been reached for other ensuing drills."
Some 17,500 US military personnel were due to take part in the Freedom Guardian drills.
"We are still coordinating additional actions. No decisions on subsequent war games have been made," Pentagon spokeswoman Dana White said in confirming the suspension.
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"There is no impact on Pacific exercises outside of the Korean Peninsula."
White said US Defense Secretary Jim Mattis, Secretary of State Mike Pompeo and National Security Advisor John Bolton would meet later this week at the Pentagon to discuss the issue.
Last week, Trump said the US would halt "war games" with its South Korean security ally - without making clear when the freeze would begin.
The US leader raised eyebrows by describing the exercises as "provocative" - a term used by the North.
US and South Korean forces have been training together for years, and routinely rehearse everything from beach landings to an invasion from the North, or even "decapitation" strikes targeting the North Korean regime.
Pyongyang typically reacts furiously. Following drills last year, the North fired ballistic missiles over Japan, triggering global alarm.
At their landmark Singapore summit, Trump and Kim signed a joint statement in which North Korea committed to "work toward complete denuclearisation of the Korean Peninsula."
But critics have pointed to the vague wording of the non-binding document and raised fears that the summit would weaken the international coalition against the North's nuclear programme.
Pompeo, who has stressed that sanctions would remain in place until North Korea's complete denuclearisation, said he plans to meet Kim for follow-up talks.
South Korea said sanctions against North Korea could be eased once it takes "substantive steps towards denuclearisation," seemingly setting the bar lower than Washington for such a move.
But Pompeo's office said both allies remain "committed to the goal of complete, verifiable and irreversible denuclearisation."
