The report by Pyongyang's official Korean Central News Agency on Sunday came a day after South Korea's military said it detected the North launching several unidentified short-range projectiles into the sea off its eastern coast.
The agency says Kim expressed "great satisfaction" over Saturday's drills and stressed frontline troops to keep a "high alert posture" and enhance combat ability to "defend the political sovereignty and economic self-sustenance of the country."
U.S. President Donald Trump says he still believes a nuclear deal with North Korea will happen, after the country fired several unidentified short-range projectiles into the sea.
Trump tweeted Saturday that he believes that leader Kim Jong Un "fully realizes the great economic potential of North Korea, & will do nothing to interfere or end it."
Added Trump: "He also knows that I am with him & does not want to break his promise to me. Deal will happen!"
A diplomatic summit between Trump and Kim over the North's pursuit of nuclear weapons broke down earlier this year without a deal. North Korea wants widespread sanctions relief in return for disarmament moves that the United States has rejected as insufficient.
South Korea says it's "very concerned" about North Korea's weapons launches, calling them a violation of last year's inter-Korean agreements to reduce tensions between the countries.
The South Korean government says it urges North Korea to stop committing acts that would raise military tensions and join efforts to resume nuclear negotiations.
South Korea says it's working with the United States to find out details of the launches such as what type of projectiles North Korea fired earlier Saturday.
The South Korean statement came after a meeting of the presidential national security adviser, the defense minister, the intelligence chief and other officials following the North Korean launches at the presidential Blue House.
The United States and South Korea are analyzing North Korea's short-range missile launches while "carefully responding" to Pyongyang's action.
That's according to South Korean Foreign Ministry statement following telephone talks between U.S. Secretary of State Mike Pompeo and his counterpart in Seoul.
Later Saturday, South Korean Foreign Minister Kang Kyung-wha also talked by phone with Japanese Foreign Minister Taro Kono and they agreed to keep coordinating while also "carefully responding" to the launches.
Japanese Foreign Minister Taro Kono and U.S. Secretary of State Mike Pompeo have held telephone talks after North Korea launched several unidentified short-range projectiles into the sea.
Japan's Foreign Ministry says Kono, who is currently visiting Angola, and Pompeo talked for about 10 minutes Saturday and confirmed the two sides will share information on the development and stay in close contact.
The two ministers also agreed to cooperate with South Korea.
Japan's Defense Ministry says the projectiles weren't a security threat and didn't reach anywhere near the country's coast.
Japan will likely avoid any harsh response as Prime Minister Shinzo Abe seeks to secure his own summit with Kim Jong Un.
The White House says it is monitoring North Korean short-range missile launches.
In a terse statement, Press Secretary Sarah Sanders says, "We are aware of North Korea's actions tonight. We will continue to monitor as necessary."
South Korea's Joint Chiefs of Staff says that North Korea early Saturday launched several short-range missiles off its eastern coast into the ocean.
If it's confirmed that the North fired banned ballistic missiles, it will be the first such launch since the North's November 2017 test of an intercontinental ballistic missile.
Japan's Defense Ministry says North Korean missiles have not reached anywhere near the country's coast and that Japan is not facing any security threat.
The ministry says it has not detected signs that any of the North Korean short-range missiles fired Saturday have reached in or around Japan's territory or its 200-nautical-mile (320-kilometer) exclusive economic zone.
It says at this point Japan does not face a situation that would pose any immediate risk to its national security.
Japan is seen as avoiding any harsh response as Prime Minister Shinzo Abe seeks to secure a summit with North Korean leader Kim Jong Un.
South Korea's Joint Chiefs of Staff says that North Korea has launched "several" short-range missiles off its eastern coast.
The military said in a statement Saturday that the missiles flew up to 200 kilometers (125 miles) before they landed in the water.
The South had previously said the North launched a single missile.
The South Korean Joint Chiefs of Staff says North Korea has fired an unidentified short-range missile from its eastern coast.
The firing Saturday comes amid a diplomatic breakdown that has followed the failed summit earlier this year between President Donald Trump and North Korean leader Kim Jong Un over the North's pursuit of a nuclear arsenal that can target the U.S. mainland.
The Joint Chiefs of Staff says the North's missile was fired from Wonsan on the east coast.
It says South Korean and U.S. authorities are analyzing the details of the launch.