(CNN) Could a prisoner handover spare the lives of two ISIS hostages?

A message purporting to be from the Islamist terror group sets a new deadline for a possible deal with the Jordanian government.

The latest demand: Bring convicted terrorist Sajida al-Rishawi to the Turkish border by sunset Thursday, or Jordanian ISIS hostage Moaz al-Kassasbeh will be executed "immediately."

But is ISIS offering anything in return?

From the latest message, it's unclear. But previous video posts purportedly from ISIS have suggested the group was offering Japanese hostage Kenji Goto's freedom in exchange for al-Rishawi's.

CNN could not independently confirm the authenticity of the latest message, which was read by a person claiming to be Goto and posted online by ISIS supporters. In the message, Goto purportedly calls for al-Rishawi's release in "exchange for my life."

It's the latest twist in a complicated crisis with dizzying developments involving several countries. Here's a look at the key people involved:

JUST WATCHED Japan on edge as it awaits word on ISIS hostage Replay More Videos ... MUST WATCH Japan on edge as it awaits word on ISIS hostage 01:58

• Goto, an experienced Japanese war journalist, has been at the center of several threats by ISIS since his capture. Last week, the group demanded $200 million from Japan in exchange for Goto and fellow Japanese hostage Haruna Yukawa, an aspiring security contractor. Since then, ISIS has claimed Yukawa is dead , but Goto is still alive.

• Al-Kassasbeh, a Jordanian pilot, was captured by ISIS last month after the fighter jet he was flying crashed in Syria. ISIS says he's still alive, but Jordan's foreign minister told CNN his government has asked for a proof of life, but hasn't received it.

• Al-Rishawi is an Iraqi prisoner on death row in Jordan for her role in 2005 bombings. ISIS has demanded her release by sunset Thursday (5:30 p.m. in Mosul, Iraq; 9:30 a.m. ET). Jordan has said it's willing to swap al-Rishawi for the Jordanian pilot.

New deadline, but does swap offer stand?

Jordanian Foreign Minister Nasser Judeh told CNN on Wednesday that his country would release al-Rishawi if ISIS released al-Kassasbeh.

Even though his government's announcement of its offer doesn't mention Goto, the foreign minister said that the Japanese journalist is not forgotten.

Judeh "Of course," Goto's release would be part of a prisoner exchange,Judeh told CNN's Christiane Amanpour . But the priority for Jordan is al-Kassasbeh's freedom, he said.

JUST WATCHED Why does ISIS want Sajida al-Rishawi? Replay More Videos ... MUST WATCH Why does ISIS want Sajida al-Rishawi? 02:23

It wasn't clear whether ISIS would accept Jordan's offer.

Families' anguish

With the fates of their sons hanging in the balance, the families of Goto and al-Kassasbeh called on their governments to do everything they can to save the hostages before time runs out.

Goto, 47, is reported to have three children, two of them with his current wife.

His mother begged Japanese Prime Minister Shinzo Abe to secure her son's release.

"Please save the life of Kenji," Junko Ishido said. "I call on you to work with all your strength in negotiations with the Jordanian government, until the very end."

Al-Kassasbeh's father has called on Jordanian authorities to act as well.

"I firmly ask whomever has sent Moaz to fight outside the borders of Jordan, on a mission unrelated to us, to make strong efforts to bring back Moaz," Safi al-Kassasbeh said Tuesday.

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ISIS says it captured al-Kassasbeh after he ejected from his F-16 jet last month near Raqqa, the militant group's de facto capital in Syria.

"Moaz's blood is precious, it's precious and it represents the blood of all Jordanians," his father said.

But the pilot's father suggested his son's case shouldn't be mixed up with Goto's.

"To link Moaz's situation with the Japanese journalist, this has nothing to do with us," he said. "The Japanese journalist has his country to defend him."

Grim track record

ISIS, which holds large areas of Iraq and Syria under its brutal rule, has a grim track record of ruthlessly killing hostages. Last year, it publicized its series of beheadings of three American and two British captives.

The group has made a series of demands regarding the Jordanian and Japanese hostages.

In a Saturday post purportedly from ISIS, a voice thought to be Goto's first set out the idea of exchanging him for al-Rishawi, but no clear deadline was mentioned. In that post, Goto held a photo of what appeared to be Yukawa's decapitated corpse.

post from the group on Tuesday announced that time was suddenly in short supply for Goto and the Jordanian pilot.

In that message, the Japanese hostage is shown handcuffed and dressed in orange, holding a picture that appears to be al-Kassasbeh. "I've been told this is my last message," a voice purporting to be that of Goto says, demanding the prisoner exchange. The video had said that ISIS would kill al-Kassasbeh and Goto within 24 hours if Jordan did not release al-Rishawi.

JUST WATCHED ISIS demands hostage swap Replay More Videos ... MUST WATCH ISIS demands hostage swap 02:02

CNN couldn't independently verify the authenticity of the messages. The Japanese government said there was no evidence so far that it wasn't Goto speaking in Tuesday's video, which was posted to YouTube and distributed on social media by known ISIS supporters.

On Thursday, Japan's prime minister told lawmakers his government was analyzing the latest possible message from ISIS.

"Given the nature of the issue, we cannot tell concrete details," Abe said. "However, within this extremely severe context, the government (of Japan) has been requesting cooperation from the government of Jordan and will continue making the utmost effort for swift release of Mr. Goto."