The projectile was sacked from the Sino-ri location north-west of the capital, Pyongyang, toward the east, according to South Korea's Joint Chiefs of Staff. Details from the meeting weren't immediately announced.
Pyongyang, Seoul and Washington have refrained from calling Saturday's launch a missile, which could jeopardise the ongoing diplomacy by violating UN Security Council resolutions as well as Kim's promise of a freeze on long-range missile tests.
"We urge North Korea to stop the act of heightening military tensions on the Korean peninsula".
In a phone call on Tuesday following Saturday's launch, Trump reportedly encouraged South Korean President Moon Jae-in to continue providing food aid to the North - a crisis both South Korea and the United States say Pyongyang has manufactured - saying it is "timely and will be a positive move", according to South Korea's Chosun Ilbo newspaper.
North Korean First Vice Foreign Minister Choe Son Hui, a key figure in the nuclear negotiations with the United States, warned late last month of an "undesired consequence" for the US if Washington does not adjust its policy on North Korea's denuclearization by an end-of-the-year deadline Kim has set.
"The test comes as U.S. envoy on North Korea Stephen Biegun is visiting Seoul", NPR's Anthony Kuhn reports from South Korea's capital, "and defense officials from the U.S., Japan and South Korea are holding annual talks here, as well".
Some observers said North Korea could fire more missiles, including those of a medium range, to up the pressure on the United States.
North Korea declared in April 2018 that it would discontinue nuclear tests and inter-continental ballistic missile tests. Anything fired from it in an easterly direction would have to cross the Korean peninsula before reaching the sea.
But their second summit in Vietnam in February broke up without an agreement rolling back Pyongyang's nuclear programme in exchange for sanctions relief or even a joint statement, leaving the North frustrated.
There was no immediate comment from North Korea or the United States.
The ship, the M/V Wise Honest, was "used to illicitly ship coal from North Korea and to deliver heavy machinery to the (Democratic People's Republic of Korea)", the Justice Department said, alleging that "payments for maintenance, equipment, and improvements of the Wise Honest were made in United States dollars through unwitting U.S. banks".
It also appeared to hint at the possibility of more weapons tests, saying: "The south Korean military were astonished by the recent strike drill".
North Korea fired off two short-range missiles, according to officials in South Korea on May 9.
"I suspect that it was either an Iskander or a clone of the Iskander that the North Koreans have somehow built", he said. Images of the fired weapons indicate that one of the weapons was a short range ballistic missile.