Jordan's security and military agencies were making constant checks to see whether the pilot, Muath al-Kasaesbeh, was still alive, government spokesman Mohammad al-Momani said.
Kasaesbeh was captured in December after his F-16 fighter jet crashed in territory controlled by the militants in Syria.
"We are still ready to hand over the convict Sajida al-Rishawi in return for the return of our son and our hero," Momani told Reuters.
There has been public pressure on Jordan to negotiate with Islamic State, an offshoot of al Qaeda which has seized territory in Syria and Iraq. Protests have erupted in Karak, home town of the pilot, who is from an important Jordanian tribe that forms the backbone of support for the Hashemite monarchy.
Jordan's government also condemned the purported beheading of Japanese journalist Kenji Goto, shown in an Islamic State video released late on Saturday. Goto had been held captive along with Kasaesbeh but the footage made no mention of the Jordanian.
A palace statement said that King Abdullah received a phone call from Japanese Prime Minister Shinzo Abe thanking him for his efforts to try to secure the release of Goto "who was killed in cold blood and without any justification".
The monarch was also quoted as saying the "cowardly criminal act" was rejected by all laws and had nothing to do with Islam.
Islamic State has demanded the release of Rishawi in exchange for the pilot's life. She was jailed by Jordan for her role in a 2005 suicide bomb attack that killed 60 people in the capital Amman.
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