Jordan offered on Wednesday to hand over an Iraqi woman on death row for her role in a 2005 suicide bomb attack if a Jordanian pilot captured by the Islamic State (IS) was released.
Government spokesman Mohammad al-Momani made no mention of Japanese hostage Kenji Goto, a veteran war reporter who is also being held by the militant group.
"Jordan is ready to release prisoner Sajida al-Rishawi if the Jordanian pilot Lieutenant Muath al-Kasaesbeh is released and his life spared," Momani was quoted as saying on state television.
Kasaesbeh was captured after his jet crashed in northeastern Syria in December during a bombing mission against Islamic State.
His fate was thought to be tied to that of Goto after a video was released on Tuesday purporting to show the Japanese national saying he had 24 hours to live unless Jordan released al-Rishawi.
The voice on the video said Kasaesbeh had a shorter time to live. Japan confirmed the existence of the video at 11 p.m. (1400 GMT) on Tuesday. Momani said Jordan's priority was to secure the release of the pilot, who hails from an important Jordanian tribe that forms the backbone of support for the Hashemite monarchy.
Several hundred people, including Kasaesbeh's relatives, gathered in front of the office of Jordan's prime minister on Tuesday, urging authorities to meet the demands of Islamic State.
Al-Rishawi has been held in Jordan over her role in a suicide bombing that killed 60 people in the capital Amman.
In Japan, a spokesman at Prime Minister Shinzo Abe's office said he had no immediate comment on the Jordanian statement.
The hostage taking presents Abe with his biggest diplomatic crisis since he took power in 2012, and there has been a flurry of unconfirmed reports in Japanese media that a swap deal involving Goto might be in the works.
Goto's mother, speaking shortly after the presumed deadline had passed late on Wednesday, said: "My emotions are all over the place.
"A time limit has been set, and that has made me nervous," Junko Ishido told reporters at her Tokyo home.
She had earlier urged the Japanese government to do its utmost to save his life and reiterated that her son was not an enemy of Islam.
Abe said Tuesday's video was "despicable". He called on Jordan to cooperate in working for Goto's quick release, but vowed Tokyo would not give in to terrorism.
Goto went to Syria in late October. According to friends and business associates, he was attempting to secure the release of Haruna Yukawa, his friend and fellow Japanese citizen who was captured in August.
In the first of three videos purportedly of Goto, released last week, a black-clad masked figure with a knife said Goto and Yukawa would be killed within 72 hours if Japan did not pay Islamic State $200 million.
The captor resembled a figure from previous Islamic State videos whose threats have preceded beheadings.
A video on Saturday appeared to show Goto with a picture of a beheaded Yukawa, saying his captors' demands had switched to the release of al-Rishawi.
Tuesday's video featured an audio track over a still picture that appeared to show Goto holding a picture of now bearded Kasaesbeh.
Officials involved in the crisis say Tokyo knew for months that Islamic State militants were holding two Japanese men captive, but appeared ill-prepared when the group set a ransom deadline and purportedly killed one of them.