The hostage crisis has become a test for Prime Minister Shinzo Abe, who took power in 2012 pledging to bolster Japan's global security role.
Abe on Sunday condemned the killing of Japanese citizen Haruna Yukawa by the militants as "outrageous" and called for the release of veteran correspondent Kenji Goto, captured by Islamic State militants in Syria.
"We would like to work together with the Jordanian government to secure the release of Goto," Yasuhide Nakayama, state minister for foreign affairs, told reporters in Jordan late on Monday.