AMMAN, Jordan — Jordan is willing to swap an Iraqi woman prisoner involved in deadly 2005 hotel bombings 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 hardline approach toward Islamic militants and to the position of its main ally, the United States, of not negotiating 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.

On Wednesday, 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.” His comments were carried by Jordan’s official Petra news agency.