Trump tweeted that Kim's letter, which he had earlier described Friday as very personal, tied the continued missile tests to the joint exercises.
In the foreign ministry statement carried by KCNA, Pyongyang said Seoul had "defiantly staged an aggressive war exercise against us".
North Korea has long denounced the annual exercises, which it considers rehearsals for an invasion despite allied assurances that the drills are defensive in nature.
"Kim knows that he can continue to launch these short-range missiles without consequences".
North Korean state media says Saturday's launch of two projectiles was a test to verify the capabilities of a new weapons system.
North Korea has been carrying out the tests to express its anger at a joint military drill the US and South Korea are scheduled to begin on Sunday and to gain leverage in bilateral talks that Washington hopes to start soon with the North, analysts said. "It was. also a small apology for testing the short range missiles, and that this testing would stop when the exercises end", Trump tweeted. Talks have stalled since the collapse of Mr. Trump's second summit with Kim in Vietnam in February over disagreements on exchanging sanctions relief and disarmament, although Mr. Trump made a historic trip into North Korea after the G20 conference in June.
Mr Trump reiterated that he was not bothered by the flurry of short-range weapons Mr Kim has launched despite the growing threat they pose to U.S. allies in the region.
Kwon Jong Gun, Director-General of the Department of American affairs in North Korea, said in a statement released by Pyongyang's Korean Central News Agency on Sunday, that Seoul failed to give a plausible explanation for the joint military exercise. "We should be reimbursed for it".
The North has unleashed a series of test firings of short-range weapons in recent weeks while saying that the joint military drills between the allies compel it to "develop, test and deploy the powerful physical means essential for national defence".
News of this most recent round of missile testing came shortly after Trump told reporters he received a separate "really beautiful" and "very positive letter" from the North Korean despot.
The North's recent tests have dampened the optimism that followed the third and latest meeting between Trump and Kim on June 30 at the inter-Korean border.
Trump has for decades complained that US allies such as South Korea, Japan and others are not paying enough for USA military protection.
Pyongyang has lauded Trump and his personal ties with Kim while chastising South Korea as a "puppet" regime following the orders of its master, the United States. Should Pyongyang signal increasing hostility, the USA and South Korea might do well to arrange diplomatic talks both to quell increased tension and attempt to progress in the nuclear negotiations.