Experts, however, have expressed skepticism, noting there is no way to independently verify the test results.
The warhead atop the test missile fell just 23 feet (seven meters) from its target point, according to a statement from Pyongyang's state-run Korean Central News Agency.
The KCNA report did not give a distance the missile covered, but Japanese and South Korean monitors said it flew 248 miles (400 kilometers) over the Sea of Japan/East Sea from a launch point on Wonsan, on North Korea's east coast.
KCNA said Monday's test proved its ability to launch and guide a warhead equipped "with control wings." Such a warhead, also known as a "maneuverable re-entry vehicle," enables it to make corrections in midflight for greater accuracy.
North Korea also claimed to have fired Monday's rocket from a new tracked, self-propeled vehicle, which, if true, would give Pyongyang the ability to launch missiles far quicker than compared to its previous systems.
The new missile and launch system were first displayed at a military parade in Pyongyang in April, KCNA said.
Bruce Bennett, senior international defense researcher at the Rand Corp, a California-based global policy think tank, expressed doubts about North Korea's claims of success.
Several experts say the missile tested Monday was also fired two or three times in a string of four unsuccessful tests during March and April, Bennett told CNN.
"My first inclination is to assume that the North Korean missile was not very accurate. After all, Kim Jong Un was anxious to sustain a pattern of missile test successes after so many failures from late March through April," he said.
Monday's missile launch was North Korea's third such test in less than three weeks.
North Korea has fired 12 missiles during nine tests so far in 2017
-- this compares with 10 missile launches in the same time period in 2016.
Analysts say all of North Korea's tests, successful or not, provide information that help bring it closer to its goal of building a missile that could reach the US.
North Korea has dubbed its last three tests successes. And analysts did call a May 14 test Pyongyang's best ever.
But Bennett says future success is far from guaranteed.
"As North Korea demonstrated last year with its tests of the Musudan missiles, one successful launch after a series of failures does not mean that the missile will always work thereafter. With the Musudan tests, there were five failures, then a success, then two more failures," he said.
Monday's missile test drew immediate protests from Japan and South Korea, with Japanese Prime Minister Shinzo Abe promising "concrete action" in response to the test, and South Korean defense chiefs saying the North would face "strong punishment from our military."
US President Donald Trump tweeted that North Korea showed "great disrespect" for longtime ally China with the test.
China has called on Pyongyang to suspend its nuclear and missile testing while calling on the US to stop military exercises on and near the Korean Peninsula which North Korea sees as a threat to its sovereignty.
KCNA cited one of those exercises on Tuesday, saying a day earlier the US Air Force flew B-1 bombers from Guam over South Korea in what the North called "a grave military provocation."
US military officials confirmed two B-1s flew over South Korea on Monday. The presence of US bombers "provides assurances to our allies and strengthens security and stability," said US Lt. Col. Lori Hodge.
Bennett said the frequency of Kim's missile testing may indicate some instability in North Korea, perhaps some discontent with the regime from North Korean elites.
"His insistence on repeated tests, despite even China being unhappy with the tests, suggests that he has something to prove internally," Bennett said.