Trump announced he had fired Bolton a day after North Korea signaled a new willingness to resume stalled denuclearization talks, but it then proceeded with the latest in a spate of missile test launches.
He said the weapons system "has been finally verified in terms of combat operation" and "running fire test" is what remains to be done.
While analysts said North Korea conducts weapons tests for a range of purposes, including technical development and reassurance for the defence establishment, Tuesday's launches appeared to have been timed to send a message to Washington regarding what may happen if the USA does not come to North Korea with realistic proposals.
The test looked to be of a 600mm calibre multiple-launch rocket system that North Korea first introduced last month, said adjunct senior fellow Ankit Panda at the Federation of American Scientists.
While offering talks, North Korea still warned its dealings with the US may end if Washington fails to come to the negotiating table without new acceptable proposals. Some experts said the North Korean weapons tests were also a demonstration of its expanding weapons arsenal aimed at boosting its leverage ahead of new talks with the United States.
Trump had been growing more impatient with the failure to oust socialist Venezuelan President Nicolas Maduro through a USA -led campaign of sanctions and diplomacy in which Bolton was a driving force.
A missile blasts off in Kaechon, South Pyongan Province on Tuesday, in this image from the [North] Korean Central News Agency on Wednesday. North Korea often ratchets up military tensions ahead of negotiations meant to end its nuclear ambitions.
North Korea said on Monday it was willing to restart nuclear talks with the United States in late September but warned that dealings between the sides could end unless Washington takes a fresh approach.
Little progress has been made in getting Kim to give up his weapons programs, but Trump has repeatedly pointed to North Korea's freeze in nuclear and long-range missile tests since 2017 as evidence of the success of his efforts.
North Korea's official media has repeatedly denounced U.S. Secretary of State Mike Pompeo and urged Trump to replace him with a "more mature" interlocutor.
Choe said she hopes the United States will bring "a proposal geared to the interests of the DPRK and the USA and based on decision methods acceptable to us".
US -led diplomacy aimed at stripping North Korea of nuclear weapons collapsed after the second summit between Kim and President Donald Trump in Vietnam in February ended without any agreement due to disputes over USA -led sanctions on the North. Kim and Trump met again at a Korean border village in late June and agreed to resume talks.