Jordan's government said today that it is prepared to hand over Sajida al-Rishawi, an Iraqi woman on death row since 2005, to the Islamic State in exchange for Muadh "Maaz" al-Kasesbeh, the Jordanian pilot held hostage by the extremist group since last December.

"Jordan is ready to release the Iraqi prisoner Sajida al-Rishawi, if the Jordanian pilot al-Kasesbeh is released unharmed," spokesman Mohammed al-Momani said, responding to a demand from the militant group in a video on Tuesday.

The pilot's relatives and supporters held a rally for his release in Amman today, holding signs in Arabic that read "We are all Maaz."

Momani's statement came as the 24-hour deadline imposed by the Islamic State for Rishawi's release was fast approaching. The militants communicated the time limit to Jordan in Tuesday's video message, featuring the Japanese war reporter Kenji Goto, also held captive by the extremists since October.

The video shows a picture of Goto holding a photo of Kasesbeh, while a voiceover purportedly by the journalist warns the Japanese government that he and the pilot do not have long left to live unless Jordan frees Rishawi.

The voice says: "The only barrier between me and my freedom is now just the Jordanian government, and the delaying handover of Sajida.

It adds: "Tell the Japanese government to put all their political pressure on the Jordanian government. Time is now running very short. It is me for her, what is so difficult to understand. Her for me — a straight exchange.

"Any more delays by the Jordanian government will mean they are responsible for the death of their pilot, which will then be followed by mine. I only have 24 hours left to live, and the pilot has even less."

Japan's Prime Minister Shinzo Abe reacted to the new threats posed by the Islamic State on Wednesday morning. "This was an extremely despicable act and we feel strong indignation. We strongly condemn that", said Abe.

On Wednesday morning, Goto's mother appealed to the government, begging Abe to work with Jordan as long as it takes to save her son.

Momani's statement, however, does not make any reference to the Japanese journalist, only mentioning an exchange between Kasesbeh and Rishawi. Nevertheless, Japanese media were camped out at Syria's border with Jordan on Wednesday in anticipation of a possible release, as a new video emerged purporting to be from the Islamic State and claiming the two hostages were both to be freed. It could not be independently verified.

Rishawi, referred to as an "imprisoned sister" by the Islamic State, was involved in a suicide bombing operation in Amman that killed 60 people at a wedding in 2005, but her device failed to detonate. She was then arrested by the Jordanian authorities and sentenced to death, after confessing to her role in the attack on Jordanian state television. In 2006, however, Jordanian government decided to suspend the death penalty until last month and Rishawi has remained in Jordan as a prisoner for almost 10 years.

Her brother was a close aide to the late leader of Abu Musab al-Zarqawi, the late leader of al-Qaeda in Iraq, the group which gave birth to the Islamic State. He and two other brothers were reportedly killed in Iraq fighting US forces.