The missile launch comes days after Russia vetoed a United Nations resolution that monitors enforcement of nuclear sanctions against the North Korean government.
North Korean leader Kim Jong Un also recently encouraged his military to prepare for a potential war. At the end of March, Japanese Prime Minister Fumio Kishida offered to meet with Kim "as soon as possible" to address tensions.
Senior official Kim Yo Jong replied by saying that there would be no breakthrough improvement in North Korea-Japan relations.
"The history of the DPRK-Japan relations gives a lesson that it is impossible to improve the bilateral relations full of distrust and misunderstanding, only with an idea to set out on a summit meeting," Kim Yo Jong said.
"If Japan truly wants to improve the bilateral relations and contribute to ensuring regional peace and stability as a close neighbor of the DPRK, it is necessary for it to make a political decision for a strategic option conformed to its overall interests."
Reuters and The Associated Press contributed to this report.