The communist nation launched several ballistic missiles, including a long-range Taepodong-2, late Tuesday despite a moratorium on missile tests. The Japanese military said at the time that all missiles fell in the northwestern part of the Sea of Japan closer to Russia than to Japan.
The embassy said the two ministers had held talks on the issue earlier in the day.
It also said Japan had submitted a draft resolution on the launches to the UN Security Council that is backed by most members except Russia and China.
"We believe that resolute reciprocal actions will, on the contrary, return North Korea to the negotiations. If we give no resolute response, we will thus send a wrong signal to North Korea," the embassy said.
The embassy also said Japan expected leaders of the Group of Eight industrialized nations to issue a strong statement on the missile launches.
"This issue should be discussed during the G8 summit [in St. Petersburg on July 15-17]," the embassy said. "We hope that G8 leaders will send a very strong message to North Korea."