The North has not publicly tested any weapons since November 2017, but in recent days Pyongyang reportedly expressed anger at US-led international sanctions and ongoing small-scale military drills between South Korea and the United States.
Earlier this month, North Korea's Foreign Ministry warned it could bring back its policy of bolstering its nuclear arsenal if it does not receive sanctions relief.
Shin Beomchul, an analyst of Seoul's Asan Institute for Policy Studies, said:
"It's North Korea-style coercive diplomacy. North Korea is saying 'If you don't listen to us, you will face political burdens'."
Mr Shin said the weapon North Korea tested could be a missile, artillery, an anti-air gun, a drone or other high-tech conventional weapons systems.
Asked about the test, the US State Department said that American and North Korean officials are talking about implementing the commitments that Mr Trump and Mr Kim made during their June meeting in Singapore.
Eugene Lee, the spokeswoman of South Korea's Unification Ministry, declined to comment on Mr Kim's inspection of the weapons test.
US vice president Mike Pence, attending a Southeast Asian summit in Singapore, cited the "great progress" made on North Korea but said more had to be done.
A year and a half ago, "nuclear tests were taking place, missiles were flying over Japan and there were threats and propagations against our nation and nations in the region," Mr Pence said.
"Today, no more missiles are flying, no more nuclear tests, our hostages have come home, and North Korea has begun anew to return fallen American heroes from the Korean War to our soil. We made great progress but there's more work to be done," he said.
Mr Pence stressed that UN sanctions had to remain enforced.