"The release of this pilot as soon as possible is also an issue for us Japanese," Nakayama said.

"Both our nations have to work together to ensure that both the pilot and the Japanese hostage return to their respective homes with smiles on their faces."

Media has reported that the militants were demanding the release of another death-row convict, raising speculation about multiple swaps involving Goto and the Jordanian pilot.

Jordan's King Abdullah was quoted as telling a Jordanian newspaper that the case of the pilot, First Lieutenant Muath al Kasaesbeh, "tops the country's priority".

In Tokyo, Abe told parliament on Tuesday that Japan would do its utmost to save Goto.

"The horrible act of terrorism by ISIL is outrageous and we resolutely condemn it," Abe said, referring to the militants.

"The situation is extremely severe but we'll do the utmost to have Kenji Goto released as soon as possible ... We won't give in to terrorism."

Two members of Jordan's parliament told Kyodo news agency on Monday that Jordan may be willing to release al-Rishawi in exchange for Goto and Kasaesbeh.