Mr Abe called on minsters to ensure the safety of all Japanese people abroadJapan's Prime Minister Shinzo Abe has said a new Islamic State (IS) video threatening to kill hostage Kenji Goto within 24 hours is "despicable".
In the footage a voice believed to be Mr Goto says he and a Jordanian pilot will be killed unless Jordan frees an Iraqi woman held on death row.
Mr Abe said Japan was working with Jordan to secure their release, bbc reports.
IS said on Sunday it had killed another Japanese man, Haruna Yukawa. It had demanded a $200m (£130m) ransom.
In the latest footage, released around midday on Tuesday, the speaker says Mr Goto has "only 24 hours left to live" and Jordanian hostage Mu'ath al-Kaseasbeh "even less" unless Jordan releases Sajida al-Rishawi.
Al-Rishawi is an al-Qaeda militant who has been sentenced to death in Jordan for her involvement in a 2005 attack that killed 60 people.
Kenji Goto, 47, is a well-known freelance journalist and documentary film-maker who went to Syria in October, reportedly to try to secure the release of fellow Japanese national Haruna Yukawa.
A video appeared on Sunday apparently showing Mr Goto holding a picture of what appeared to be the body of Mr Yukawa.
Speaking to reporters at the start of a cabinet meeting on Wednesday morning, Mr Abe said he was appalled by the "utterly despicable" videos, and that the government was asking for Jordanian co-operation.
He called on ministers to "take all possible measures to ensure the safety of Japanese nationals at home and abroad," the AFP news agency reports.
The mother of Mr Goto appealed publically to the prime minister to help her son.
"Please save him," she said. "Kenji has only a little time left."