North Korea published photos after the test that demonstrated "a very challenging technology for us" to detect before launch, he said.
"We have the readiness and ability to counter any challenge from the United States", he was quoted as saying.
These launches defy United Nations resolutions that ban North Korea from any use of ballistic missile technology whatsoever.
It could send another strong warning message to North Korea which is continuing its nuclear and missile development prohibited by the global community, Yonhap News Agency quoted the sources as saying.
"If I were Tillerson and the Chinese said look we are anxious about this or that".
The pair spoke by phone a day after Pyongyang fired a ballistic missile into the Sea of Japan, in what analysts said was a warning ahead of a US-China summit at which North Korea s accelerating atomic weapons program is set to top the agenda.
The phone conversation between Trump and Abe took place as a ballistic missile test by North Korea drew condemnation from countries in the region and a USA missile strike in Syria ratcheted up tensions with Russian Federation.
The United States, Japan and South Korea are working toward thwarting North Korea's possible plans of conducting its sixth nuclear test this month.
South Korea is protected under an American security umbrella and is home to thousands of United States troops.
Japan officially lists 17 nationals as abduction victims but suspects North Korea's involvement in more disappearances.
News reported on Friday that U.S. President Donald Trump is considering the options presented to him by the National Security Council on how to respond to Pyongyang's nuclear program.
The US and Chinese leaders are expected to discuss the growing threat from Kim Jong-un's nuclear programme during their meeting later on Thursday.
Trump, since coming to power in January, has been careful to assure Japan that the U.S., which guarantees Tokyo's security, has its back in the face of North Korean provocations.
In response, Secretary of State Rex Tillerson only offered a 23-word statement: "North Korea launched yet another intermediate range ballistic missile".
North Korea also mentioned unilateral USA sanctions as a cause for instability and described the embargoes as "hostile actions" against the regime.
The launch was North Korea's latest in a long series of missile and nuclear tests that have accelerated in their variation and intensity over the last two years.
The rapid advancement of the North Korean nuclear program has put the USA under increasing pressure in recent months.
More important, he must convince the Chinese leader that Beijing's short- and long-term strategic interests are better served by a denuclearized, peaceful and prosperous Korean Peninsula, and the best way to achieve this is an economic crackdown on Pyongyang by Beijing, forcing it to give up its ballistic missiles and nuclear weapons.