Junko Ishido, mother of journalist Kenji Goto, read to reporters her plea to prime minister Shinzo Abe, which she said she sent after both Mr Abe and the main government spokesmen declined to meet her because their schedules were full.
“Please save Kenji’s life,” Mrs Ishido said, begging Mr Abe to work with the Jordanian government to save Mr Goto.
“Kenji has only a little time left,” she added.
The effort to free Mr Goto and a captured Jordanian pilot, Lieutenant Mu’ath al-Kaseasbeh, gained urgency with the release of an apparent ultimatum late on Tuesday from the Islamic State group.
SCOTSMAN TABLET AND MOBILE APPS
In the message, the extremists said the two hostages would be killed within 24 hours unless Jordan frees Sajida al-Rishawi, an Iraqi woman sentenced to death in Jordan for her involvement in a 2005 terrorist attack on a hotel that killed 60 people.
Yasuhide Nakayama, a Japanese envoy for the crisis in the Jordanian capital, Amman, said only that talks on securing Mr Goto’s release were “ongoing”.
“I don’t have any information that I can share with you at the moment,” he said when asked about possible “good developments”. “There are various reports but I don’t know at all if they are true.
“We will never give up until our Japanese hostage Mr Goto comes back. We will pray for him. We will never give up.”
In Tokyo, chief government spokesman Yoshihide Suga said: “We are doing everything we can.”
Mr Abe earlier expressed outrage at Islamic State’s threat.
“This was an extremely despicable act and we feel strong indignation. We strongly condemn that,” he said.
“While this is a tough situation, we remain unchanged in our stance of seeking help from the Jordanian government in securing the early release of Mr Goto.”
The Jordanian pilot’s father, Safi al-Kaseasbeh, beseeched his government “to meet the demands” of the Islamic State group.
“All people must know, from the head of the regime to everybody else, that the safety of Mu’ath means the stability of Jordan, and the death of Mu’ath means chaos in Jordan,” he said.
About 200 of the pilot’s relatives protested outside the prime minister’s office in Amman, chanting anti-government slogans and calling on it to meet the captors’ demands.
The chairman of the foreign affairs committee of Jordan’s parliament, Bassam al-Manaseer, said that the country was in indirect talks with the militants through religious and tribal leaders in Iraq to secure the hostages’ release. He said Jordan and Japan would not negotiate directly with Islamic State and would not free al-Rishawi in exchange for Mr Goto only.
Jordan’s main ally, the United States, opposes negotiating with extremists, but Mr Manaseer’s comments were the strongest suggestion yet that Japan and Jordan might be open to a prisoner exchange.
The militants reportedly have killed one Japanese hostage, Haruna Yukawa.
Although many in Japan are critical of the two men for going to Syria, Mr Goto’s supporters have launched a social media campaign calling for his release.