Jordan has offered a prisoner swap to the Islamic State of the Iraq and the Levant (ISIL) group in an attempt to save a Jordanian air force pilot who the fighters captured and have threatened to kill along with a Japanese hostage.

Mohammed al-Momani, Jordanian government spokesperson, said on Wednesday that Jordan is ready to trade Sajida al-Rishawi, an Iraqi woman convicted of involvement in deadly Amman hotel bombings in 2005, for Moaz al-Kasasbeh, the pilot.

Efforts to release Kasasbeh and Kenji Goto, a journalist, gained urgency with the release late on Tuesday of a purported online ultimatum claiming ISIL would kill both hostages within 24 hours if Rishawi was not freed.

By Wednesday evening, however, there was no word on the fate of the hostages and no sign that a swap was under way.

Momani made no mention of Goto, and it was not clear if the swap proposed by Jordan would satisfy the hostage-takers.

In his brief statement, Momani only said Jordan is willing to swap Rishawi for Kasasbeh, but not if such an exchange is being arranged.

Rishawi was sentenced to death for her involvement in the al-Qaeda attack in the Jordanian capital that killed 60 people.

Domestic pressure

Meeting ISIL's demand for the release of Rishawi would run counter to Jordan's strict approach to the armed group.

However, the government faces growing domestic pressure to bring Moaz home.

In a possible indication of a hold-up, Nasser Judeh, Jordan's foreign minister, said on his Twitter account that Jordan had not received evidence that Moaz was alive and healthy.

The scope of a possible swap and of ISIL's demands also remained unclear.

Any exchange would set a precedent for negotiating with ISIL, which in the past have not publicly demanded prisoner releases.

Jordan's main ally, the US, opposes negotiations with "terrorists".

The release of Rishawi would also be a propaganda coup for ISIL fighters who have already overrun large parts of neighbouring Syria and Iraq.

Jordan is part of a US-led military alliance that has carried out air strikes against ISIL targets in Syria and Iraq in recent months.

Family critical

Kasasbeh's family, meanwhile, is increasingly vocal in its criticism of the government.

Several dozen protesters gathered on Wednesday outside the palace of King Abdullah II in Amman, urging the government to do more to win the release of the pilot.

"Listen, Abdullah, the son of Jordan [the pilot] must be returned home," the protesters chanted.

Safi al-Kasasbeh, Kasaesbeh's father, asked to be let into the palace, shouting: "I want to see the king." The father later said he met Abdullah.

Moaz, 26, was seized after his Jordanian F-16 fighter jet crashed in December near ISIL's de facto capital, Raqqa, in Syria.

He is the first foreign military pilot the fighters have captured since the coalition began its air strikes in August.

This is the first time ISIL has publicly demanded the release of prisoners in exchange for hostages.

Previous captives may have been freed in exchange for ransom, although the governments involved have refused to confirm any payments were made.

Jordan reportedly is holding indirect talks with ISIL through religious and tribal leaders in Iraq to secure the release of the hostages.

Japanese appeal

In Tokyo, Goto's mother, Junko Ishido, has appealed publicly to Shinzo Abe, the Japanese prime minister.

"Please save Kenji's life," Ishido said, begging Abe to work with the Jordanian government until the very end to try to save Goto.

"Kenji has only a little time left," she said.

Ishido said both Abe and Japan's main government spokesman had declined to meet her.

Later, a few dozen people gathered outside Abe's official residence, holding banners expressing hopes for Goto's release.

ISIL reportedly has killed Haruna Yukawa, another Japanese hostage, and the crisis has shocked Japan.

Goto was captured in October in Syria, apparently while trying to rescue Yukawa, 42, who was taken hostage last summer.