Kritenbrink and his South Korean counterpart Yeo Seung-bae agreed on the importance of pursuing stability on the Korean Peninsula.
An artillery firing competition among mechanized units was held on Saturday, with senior government and military officials present, the official Korean Central News Agency reported.
Kim’s health has been a focus of keen outside attention in recent months because he has appeared noticeably thinner in state media photos and videos.
While launching a spate of newly developed weapons in recent weeks, North Korea has also slammed Washington and Seoul over what it calls hostility toward the North.
Responding to North Korean missile launches, Fumio Kishida said he had instructed his government to consider all options, including allowing Japanese forces to acquire pre-emptive strike capability.
The launch came hours after the U.S. reaffirmed its offer to resume diplomacy on North Korea’s nuclear weapons program.
The South Korean and Japanese militaries didn’t immediately say what kind of ballistic missile the North fired.
Seoul’s Defense Ministry said South Korean and U.S. intelligence authorities were analyzing the North Korean weapons displayed but didn’t elaborate.
The KCNA said Kim Jong Un analysed the unprecedented difficulties facing the North and called for the party's single-minded unity in developing the state economy in face of the grim situation.
Describing its anti-virus campaign was a matter of “national existence,” North Korea had severely restricted cross-border traffic and trade for the past two years despite the strain on its economy.
Kishida supports stronger Japan-U.S. security ties and partnerships with other like-minded democracies in Asia, Europe and Britain, in part to counter China and nuclear-armed North Korea.
Liaison officials from the two Koreas exchanged messages over a cross-border communication channel on Monday morning, Seoul's Unification Ministry said.
North Korea has argued its nuclear programme is meant to cope with US military threats, though Washington has said it has no hostile intent toward Pyongyang.
South Korea, Japan and the United States typically publicly confirm North Korean ballistic missile launches, which are banned by UN resolutions, soon after they occur.
Some experts say North Korea wants South Korea to persuade the United States to ease punishing economic international sanctions on it.