Chief Cabinet Secretary Yoshihide Suga held a press conference earlier on Monday.
"We will continue to coordinate with the international community to make sure they pay for this sin. We intend to pursue effective methods to thoroughly investigate the matter."
International condemnation of the killing has also been pouring in, with UN Secretary General Ban Ki-moon calling the murder "barbaric".
Condemning Goto's killing as a heinous murder, US President Barack Obama vowed to continue to take decisive action against the extremist group. British Foreign Secretary Philip Hammond has echoed that pledge.
French President Francois Hollande has also voiced indignation over the incident, vowing that France and Japan would continue to work together for peace in the Middle East.
Meanwhile, the Jordanian government, who had earlier agreed to a prisoner swap for both the Japanese and Jordanian hostages, is still working closely to secure the release of its captured fighter pilot.
The IS is demanding the release of an al-Qaida suicide bomber who is on death row in Jordan for her role in the triple hotel bombings in Amman in 2005.
For more analysis on the Japanese hostage crisis, CRI's John Artman spoke earlier with Jun Okumura, a political analyst and commentator drawing on three decades of government service and visiting scholar at the Meiji Institute for Global Affairs.
Japan Continues to Investigate after Kenji Goto's Death
