Tuesday's launches could be created to strengthen Pyongyang's negotiating hand ahead of the resumption of the nuclear talks that have been stalled since February's no-deal breakdown of a summit between U.S. President Donald Trump and North Korean leader Kim Jong-un.
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.
The North's Korean Central News Agency said Kim, accompanied by top military and ruling Workers' Party officials, supervised the two rounds of test-firings at an unidentified place on Tuesday.
He said the weapons system "has been finally verified in terms of combat operation" and "running fire test" is what remains to be done.
Tuesday's rocket launcher test was made hours after North Korea said it was willing to resume nuclear negotiations with the United States in late September.
Numerous latest missiles launched by North Korea appear to be new types created to evade interception by US, South Korean and Japanese missile-defense systems.
The North Korean projectiles fired from its South Phyongan province, which surrounds its capital city of Pyongyang, flew about 330 kilometers (205 miles) across the country and in the direction of the waters off its east coast, according to South Korea's Joint Chiefs of Staff and Defense Ministry.
North Korea is due to come into focus when the UN General Assembly meeting starts next week in NY, after a UN Security Panel report said Pyongyang was violating sanctions to help fund its weapons programme.
The test appeared to be of 600 mm caliber multiple-launch rocket system that North Korea first introduced last month, said Ankit Panda, an adjunct senior fellow at the Federation of American Scientists.
Kim, who has suspended testing of nuclear weapons and intercontinental ballistic missiles while engaged in talks with the USA, has given Trump until the end of the year to ease up on sanctions choking his state's anemic economy.
The North Korean weapons tested in the past weeks were all short-range, and the country is still keeping its promise not to carry out nuclear and long-range missile tests.
"The timing could be convenient for USA diplomacy with North Korea", said Leif-Eric Easley, a professor at Seoul's Ewha University.
Tuesday's weapons test was the eighth round of launches by North Korea since late July.
On Monday, the North's vice foreign minister Choe Son Hui said in a statement carried by KCNA that the country had "willingness to sit with the United States side for comprehensive discussions of the issues we have so far taken up" later this month, at a time and place to be determined.
Trump also said he was considering five very qualified people to replace Bolton.
FILE - President Donald Trump meets North Korean leader Kim Jong Un in Hanoi., Feb. 28, 2019.
Trump and Kim had agreed to restart working-level talks during a meeting at the Demilitarized Zone dividing the Korean peninsula in June, but those talks have yet to begin.