The South Korean military said Sunday's test was of two short-range Scud missiles with a range of about 500 kilometres (300 miles).
A despatch by the North's official KCNA news agency was unclear about the type of missile, mentioning, "tactical rockets" and "precision-guided missiles".
A few days earlier, a similar despatch had hailed the test of a new "cutting-edge" guided missile as a "breakthrough" in the North's military capability.
Pyongyang has in the past made extravagant claims about its ballistic missile capability, and experts are divided as to how far the country has gone in developing its missile systems under UN sanctions.
North Korea carries out regular missile tests, sometimes for technical reasons but often as a show of force to register its displeasure with events elsewhere.
The two latest tests come ahead of Xi's July 3-4 trip to Seoul for talks with South Korean President Park Geun-Hye.
China is North Korea's sole major ally and key economic benefactor, and the fact that Xi is visiting Seoul before Pyongyang has been seen by some as a deliberate snub.
For all its leverage, China has grown increasingly frustrated with North Korea's refusal to curb its nuclear weapons programme as well its penchant for raising regional tension.
According to KCNA, Kim argued that the missile tests "had not the slightest impact" on regional peace and security, and were in fact a guarantor of regional stability.
"Durable peace can be protected only when one is so strong that nobody dares provoke one and it can be guaranteed by one's own strength," said Kim, who personally oversaw both the latest tests.
With Xi and Park expected to discuss Pyongyang's nuclear weapons, the North's state-run newspaper lashed out at efforts to curb its nuclear ambition as a "stupid fantasy."
The ruling party's official Rodong Sinmun reiterated Monday that the atomic weapons were means of self-defense against perceived threats from the US and the South.
"It's about time for the enemies to wake up from the stupid fantasy called 'denuclearisation of the North," it said in an editorial.
"Denuclearisation of the North' is a wild dream that can never be achieved forever," it added.
Tensions between North and South Korea have been running high for months, with each accusing the other of provocations.
Most recently, the North's army threatened a "devastating strike" after the South held a live-fire drill near the flashpoint maritime border in the Yellow Sea.
In March, the two sides traded hundreds of shells across the border off the west coast after the North dropped shells in the South's waters during a live-fire drill.