Japan's prime minister has called the audio video of the murder of Japanese hostage Haruna Yukawa by Islamic State "outrageous and unacceptable".
Shinzo Abe demanded the release of a second hostage, purported to be Kenji Goto, shown in the video. Japan says it is trying to verify the footage.
Japan's chief cabinet secretary Yoshihide Suga said the video image "showing a killed Japanese person" was "an abominable and unforgivable act of violence".
There is some doubt over whether the video released on Saturday actually comes from Islamic State.
Unlike similar previous videos, the latest recording does not carry the logo of any IS media arms, and consists of an audio message with a still image. Other official videos have shown moving footage.
In a statement, Abe said Japan would not bow to terrorism. "This act of terrorism is an outrageous and unacceptable act of violence," he said.
"I again strongly demand the immediate release of Mr Kenji Goto unharmed."
Abe has said the audio video announcing the execution of Haruna Yukawa released by the Islamic State (Isis) appears to be genuine even as condemnations against the killing poured in.
Abe said the Japanese experts are scrutinising the brief tape after initial examination suggested it was authentic.
The grim-looking prime minister, in his televised remarks broadcast by NHK TV, said: "We have been looking into its authenticity, but unfortunately at the moment we cannot help saying its credibility is high."
"Considering the unbearable pain and sorrow that his family must be feeling, I am speechless."
The publication of the video, which does not show the actual execution, was in sharp contrast with the earlier execution announcements by the Isis. The video was not posted in any of the outfit's official channels nor does it bear the Isis flag.
In the audio video released by the Islamist organisation, Japanese journalist Kenji Goto, another captive, was seen holding a photograph of slain Yukawa. Goto, speaking in English, blamed Abe for failing to secure the release of the prisoners.
Goto said the Isis has dropped the ransom amount from $200 million to $100 million but wants woman prisoner Sajida al-Rishawi released in Jordan in exchange. Japan has already set up a task force in Jordanian capital Amman to deal with the situation.
When asked about the proposed prisoner exchange demanded by the Sunni extremist group, Abe refused to comment and said the government is working on the situation.
Hours after the message of the execution surfaced, on the morning of Sunday, 25 January Japan's Chief Cabinet Secretary Yoshihide Suga told reporters there has been no communication from the captors.
Meanwhile, US President Barack Obama and British Prime Minister David Cameron have condemned the apparent murder of Yukawa.
"The United States strongly condemns the brutal murder of Japanese citizen Haruna Yukawa by the terrorist group. We stand shoulder to shoulder with our ally Japan and applaud its commitment to peace and development in a region far from its shores," Obama said in a statement.
Cameron said the latest killing is "another reminder of the murderous barbarity of the terrorists" and expressed solidarity with the Japanese people.