At left is Jordanian pilot Lt. Muath al-Kaseasbeh and at right Sajida al-Rishawi, an Iraqi woman sentenced to death in Jordan.

AMMAN, Jordan — Jordan is willing to swap an Iraqi woman prisoner involved in a deadly 2005 hotel bombing for a Jordanian pilot captured in December by extremists from the Islamic State group, a government spokesman said Wednesday.

Such a swap would run counter to Jordan's hard-line approach toward Islamic militants and to the position of its main ally, the United States, not to negotiate with extremists. An exchange also would set a precedent for negotiating with Islamic State group militants who in the past have not publicly demanded prisoner releases.

However, Jordan's government faces domestic pressure to bring the pilot home, while its participation in a U.S.-led military coalition against the Islamic State group is widely unpopular among Jordanians.

The government spokesman, Mohammed al-Momani, did not say whether a swap would actually take place. He also made no mention of Japanese journalist Kenji Goto, who is also being held by the Islamic State group.

Efforts to release the pilot and the journalist gained urgency with the release late Tuesday of a purported online ultimatum claiming the Islamic State group would kill both hostages within 24 hours if the Iraqi woman was not freed.

Today, al-Momani said that “Jordan is ready to release the Iraqi prisoner, Sajida al-Rishawi, if the Jordanian pilot, Lt. Muath al-Kaseasbeh, is released unharmed.”

Al-Rishawi was sentenced to death in Jordan for her involvement in a 2005 terrorist attack by al-Qaida on hotels in Amman that killed 60 people. Her release would be a major propaganda coup for the Islamic State group.

Jordan is reportedly in indirect talks with the militants through religious and tribal leaders in Iraq to secure the hostages' release.

The chairman of the foreign affairs committee of Jordan's parliament, Bassam Al-Manasseer, has been quoted as saying that Jordan and Japan would not negotiate directly with the Islamic State group and would not free al-Rishawi for the Japanese hostage only.

Earlier today, the mother of the Japanese hostage, Kenji Goto, appealed publicly to Japan's premier to save her son.

The mother, Junko Ishido, read to reporters her plea to Prime Minister Shinzo Abe, which she said she sent after both Abe and Japan's main government spokesman declined to meet with her.

A few dozen people gathered in front of the prime minister's official residence, holding banners expressing their hopes for Goto's release.

The militants reportedly have killed one Japanese hostage, Haruna Yukawa, and the crisis has stunned Japan.