About 500 United States and South Korean marines began military drills last week that were among joint exercises indefinitely suspended in June as Seoul and Washington focused on engaging with North Korea.
The revelations, like earlier reports on the continuation of North Korea's weapons programs, highlight the challenges of securing the complete denuclearization of the Korean Peninsula.
"We are in no rush", Trump said Wednesday.
For the time being, the denuclearization pretense is continuing on both sides.
Under doveish South Korean President Moon Jae-in, Seoul has pursued a policy of engagement with its isolated, nuclear-armed neighbour, in contrast with the U.S. which insists pressure should be maintained on Pyongyang until it denuclearises.
The North has reportedly said that revealing such information would be tantamount to submitting a list of targets the USA could attack.
Analysts have long believed that North Korea had undeclared or hidden facilities in their missile programme, which has made issues related to verification and inspections a major part of working level talks between the USA and North Korea.
South Korea reportedly has about 60 guard posts - bunker-like concrete structures surrounded with layers of barbed-wire fences and manned by soldiers equipped with machine guns - stretched across the ironically named Demilitarized Zone.
Seoul said Saturday that the two Koreas have finished withdrawing troops and firearms from some of their front-line guard posts as part of their agreements to lower military tensions.
Following this, 20 of the 22 posts were totally destroyed, with each side keeping a single, empty guard post. This is true even though the North has never repudiated its plan to conquer the South by force and reunify the two Koreas under control of the North.
While the Korean militaries move ahead with tension-reducing steps, Moon is otherwise running out of goodwill gestures toward North Korea, which is under heavy USA -led sanctions over its nuclear weapons program.
They are one of the North's most-prized products - and the country sent them to South Korea in 2000 and 2007 after previous summits.
That was a repeat of a gesture in 2000, when Kim Jong Il gave South Korea's Kim Dae Jung two Pungsans to mark a summit.
Last week, talks between US Secretary Mike Pompeo and senior North Korean official Kim Yong Chol were delayed but neither countries revealed a reason for the postponement.
But despite Trump's description of progress, North Korea has repeatedly lashed out at the US and threatened to resume building up its "nuclear forces".
Last week, North Korea called off a meeting with U.S. Secretary of State Mike Pompeo in NY, and state media said on Monday the resumption of some small-scale military drills by South Korea and the United States violated a recent agreement aimed at lowering tensions on the Korean peninsula. "Ongoing conversations continue to take place".