"To all members of ISIS, Kenji [Goto] is not the enemy of ISIS. Please release him," Junko Ishido, Goto's mother, said in a statement Thursday. "There is so little time left before the deadline."
Time is of the essence: the Japanese government says it estimates ISIS' ultimatum will expire at 2:50 p.m. Friday, Tokyo time (12:50 a.m. ET Friday).
"I sincerely apologize to the Japanese government and all concerned foreign countries for all the trouble that my son has caused," Ishido said. "I have been just crying for last three days, filled with sadness. Words fail to describe how I feel. Kenji always has been a kind person ever since he was little. He was always saying, 'I want to save the lives of children in war zones.' "
Japanese officials have said they are doing their best to communicate with ISIS, but Japanese Chief Cabinet Secretary Yoshihide Suga said Thursday that Tokyo had so far heard nothing and doesn't know what situation the two hostages are in.
In a Thursday news conference, Japanese Chief Cabinet Secretary Yoshihide Suga said Japan wants to secure the hostages' safe release but will not yield to the threat of the terrorists.
He said Japan was trying to reach the ISIS captors through third parties, such as governments in the region or local tribal leaders, but has not been able to determine whether Goto and Yukawa are safe.
"We are aiming to save them as soon as possible," Suga said Thursday.
Help from Jordan?
The government of Jordan has told Japan it will do as much as possible to try to secure the release of Goto and Yukawa, according to Suga.
Jordan, one of the Arab nations taking part in the U.S.-led bombing campaign against ISIS, already has its own challenge to deal with: the militant group last month captured a Jordanian pilot
whose plane crashed in Syria.
Japanese officials have repeatedly stressed that their military, which is constitutionally forbidden from taking action other than for self-defense, isn't involved in the international airstrikes against ISIS positions in Syria and Iraq.
The masked militant speaking in the ISIS video linked the group's ransom demand to Japanese Prime Minister Shinzo Abe's recent pledge of $200 million in financial aid to countries affected by the militant group.
Suga reiterated Thursday that the funds Japan has offered are for humanitarian purposes, like helping refugees, not military purposes.
Reports of earlier, smaller ransom demand
Leading Japanese news organizations have reported, citing unidentified government sources, that Goto's wife got an e-mail in December from someone demanding $8 million to $16 million for her husband's return.
The government is trying to confirm if that e-mail came from ISIS, the reports said. If so, it could indicate the militant group is willing to accept a smaller ransom than the $200 million it had publicly demanded.
But the question is what, if anything, is Japan willing to give.
ISIS has a ruthless track record. It has released videos touting the killing of five Western hostages since August.
Abe has called ISIS' ultimatum over the two Japanese men's lives "unacceptable" and said the international community shouldn't give in to terrorists.
But he and other government officials haven't explicitly ruled out paying a ransom.
A veteran journalist
Some details have emerged about what spurred the two Japanese citizens to travel thousands of miles to the bloody Syrian conflict. While they had different professions, the two men knew and talked to each other, said Yukawa's friend Nobuo Kimoto.
Goto, an experienced freelance journalist, made a video in October near the Turkish-Syrian border before he embarked on a perilous journey into ISIS-controlled territory.
"It is my responsibility if something happens," he explained.
Goto, 47, said he was determined to cover what was happening in the region.
"Syrian people suffering three years and a half. It's enough," he said. "So I would like to get the story of what ISIS wants to do."
Alaaeddin Al Zaim, who had worked with Goto in Syria previously, says he warned him not to enter the ISIS stronghold of Raqqa. "I tell him it's not safe for you," Al Zaim told CNN.
But Goto chose to go anyway, saying, "I am not American, I am not British. I'm Japanese. I can go," Al Zaim recalled.
Before he left, Goto gave Al Zaim a slip of paper with contact information for friends and his wife, the mother of his young children.
After hearing no word from Goto for a week, Al Zaim says called the wife.
"When I called her, she's a very strong woman," he said.
An aspiring security contractor
The aims and activities in Syria of Yukawa, a 42-year-old unemployed widower, are murkier.
He originally headed to the war-ravaged country early last year with the aim of gaining combat and survival experience to bolster his plans to set up a private security company, said his friend Kimoto.
There, Yukawa met Goto, who gave him insights on how to survive there, Kimoto said. He also introduced him to rebel fighters, who are distinct from ISIS even though both are fighting against Syrian President Bashar al-Assad's forces.
Some of the rebels talked about their need for ambulances to shuttle the wounded. That plea spurred Yukawa to start raising money for this cause after returning to Japan, according to Kimoto.
"I felt a chill when he said, after returning home, (that) he felt in Syria he was really living a life," Kimoto said. "He seems to have felt satisfaction being there and living together with the locals."
Yukawa went back to Syria in July, a trip that Kimoto said he didn't know about at the time. Kimoto said he had advised his friend to focus on building up his private security company.
Yukawa was reportedly captured in August.