Jordan offered Wednesday to exchange a female jihadist for a Jordanian pilot held by the Islamic State group, whose deadline for executing the airman and a Japanese journalist is thought to have passed.
Hours later, Amman and Tokyo both anxiously awaited news on the fate of the men, as Japan's foreign minister said the situation remained "severe".
Jordan's offer came after the hostages' parents made last-ditch pleas for their lives ahead of the IS deadline for the release of the woman, a would-be suicide bomber.
"Jordan is ready to release the prisoner Sajida al-Rishawi if the Jordanian pilot is freed unharmed," state television quoted a government spokesman as saying.
"From the start, the position of Jordan was to ensure the safety of our son, the pilot Maaz al-Kassasbeh," it added.
It made no mention of Japanese hostage Kenji Goto.
In a video released Tuesday, IS threatened to kill Kassasbeh and Goto unless Rishawi was freed within 24 hours.
The Japanese government said earlier it believed the IS deadline would expire at around 1400 GMT Wednesday.
Jordanian Foreign Minister Nasser Judeh wrote on Twitter shortly before 1500 GMT that his country was still awaiting confirmation that the pilot was safe.
About an hour earlier he denied Rishawi had already been freed.
Japan has been seeking Jordan's help since an IS video released at the weekend said another Japanese hostage, Haruna Yukawa, had been beheaded.
It has already sent Deputy Foreign Minister Yasuhide Nakayama to Amman to head an emergency response team.
In Tokyo, Foreign Minister Fumio Kishida said "24 hours have passed since we confirmed the (latest) video of Mr Goto, but we haven't received any information indicating particularly major developments.
"The situation remains severe, but we will continue making the utmost effort towards his release while closely cooperating with Jordan," he told journalists.
"We need to engage in careful and meticulous scrutiny when further considering how to handle this issue."
Rishawi has been on death row since 2006 for her part in triple hotel bombings in Amman that killed 60 people.
Kassasbeh was captured on December 24 after his F-16 jet crashed while on a mission against the jihadists over northern Syria.
Jordanian officials have noted that while the IS video threatened Kassasbeh's life, it only mentioned freeing Goto in exchange for Rishawi.
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- 'At any price' -
Jordan is among a number of Arab and Western countries that have joined US-led air raids against IS, which has seized large areas of Syria and neighbouring Iraq.
The pilot's father, Safi Kassasbeh, begged the government to save his son "at any price", while Goto's mother urged Tokyo to "please save Kenji's life".
Japanese Prime Minister Shinzo Abe had earlier blasted the militants' 24-hour deadline.
"This was an utterly despicable act, and I am appalled," he told reporters.
"The government, in this extremely serious situation, has been asking for the Jordanian government's cooperation towards the early release of Mr Goto, and this policy remains unchanged," he told ministers.
Goto's mother, Junko Ishido, was at Japan's parliament Wednesday in a failed bid to meet Abe. After being refused an appointment, she issued a plea for her son's life through assembled media.
"Prime Minister Shinzo Abe," Ishido said. "Please continue your utmost efforts in negotiating with the Jordanian government until the last minute. There is not much time left."
Her anguish was mirrored in Jordan where Kassasbeh's father and several dozen members of the family's Karak tribe demonstrated outside government headquarters in Amman late Tuesday.
"We have only one request, Maaz's return at any price," Safi Kassasbeh was quoted by media as saying.
- Respected war reporter -
After initially setting a $200 million (144 million euro) ransom for Yukawa and Goto's release, IS, which rules swathes of Syria and Iraq with an extreme form of Islam, changed tack and demanded Jordan free Rishawi.
In the latest video, respected war reporter Goto is seen holding a photograph of Kassasbeh, while a voiceover, purportedly spoken by the Japanese hostage, warns Jordan is blocking his release.
However, any suggestion of a swap will likely face resistance from the United States.
Asked about recent developments, State Department spokeswoman Jen Psaki said this week a prisoner exchange was "in the same category" as paying a ransom.
IS has previously beheaded two US reporters, an American aid worker and two British aid workers, and committed numerous atrocities including mass executions, but the killing of Yukawa was the first time a Japanese has been targeted.