TOKYO (BLOOMBERG) - Islamic State in Iraq and Syria (ISIS) militants changed tactics after allegedly killing a Japanese citizen, seeking a prisoner exchange for its remaining Japanese hostage as Prime Minister Shinzo Abe said his nation won't yield to terrorists.

A video was released purportedly showing Japanese hostage Kenji Goto, a 47-year-old war correspondent, appearing to hold a picture of his beheaded countryman, Haruna Yukawa, a 42-year-old self-styled military contractor.

In the audio portion, the voice of a man claiming to be Goto pleaded in English for his life and asked for the release of a woman jailed in Jordan on accusations of attempting to take part in a suicide bombing.

There was no immediate confirmation of the authenticity of the message, although governments did not dispute it.

Yukawa was killed after Japan failed to pay a US$200 million (S$269 million) ransom by the Islamist militants' deadline. The prisoner whom the captors now want released is Sajida al-Rishawi, an Iraqi woman who was arrested after she tried to detonate an explosive belt at a wedding party at the Radisson Hotel in Amman in 2005.

"They no longer want money. So, you don't need to worry about funding terrorists," Goto said in the message, which is addressed to his wife.

"They are just demanding the release of their imprisoned sister Sajida al-Rishawi. It is simple. You give them Sajida and I will be released."

A deal is unlikely since it would involve a public concession to the militant group and strain relations with the US, a key economic and defence ally for Japan and Jordan.

Brutal Murder

"Governments are generally less inclined to support terrorist groups with prisoners versus money," said Max Abrahms, an assistant professor of political science at Northeastern University in Boston, who studies terrorism.

"There are higher costs to governments to release terrorist prisoners," he said in an interview.

US President Barack Obama issued a statement supporting Japan and calling for the release of Goto and all other hostages held by ISIS.

"The United States strongly condemns the brutal murder of Japanese citizen Haruna Yukawa by the terrorist group ISIL," Obama said, using one version of Islamic State's name.

"We stand shoulder to shoulder with our ally Japan and applaud its commitment to peace and development in a region far from its shores."

ISIS sought to punish the Japanese government after Abe pledged US$200 million in aid to help refugees and displaced people due to the conflict in Syria and Iraq, setting the ransom at the same amount.

The group set a 72-hour deadline in a Jan 20 video that showed the two men kneeling before a knife-wielding militant.

No Harm

"We call again for no harm to come to Kenji Goto and demand his immediate release," Abe said early Sunday in Tokyo.

On a six-day Middle East trip that ended the day the first video was released, Abe said in a speech in Cairo that allowing terrorism and weapons of mass destruction to spread there would impart an "immeasurable" loss on the region.

He later denounced the kidnappings as an "unforgivable" act and said his government would never cave in to terrorism, pledging to do everything otherwise possible to secure their release.

The ISIS captors demand for al-Rishawi's release isn't likely to be met, since some of the casualties were guests at a Muslim wedding including women and children, according to Abrahms.

He said killing Japanese hostages may be a mistake for the terrorist group, since to draw recruits it helps to show the violence is in response to foreign occupation. Japan doesn't have a conventional military and it has provided humanitarian assistance.

The lives of the two Japanese hostages became intertwined when they met in Syria after Yukawa travelled there for the first time last year. Goto, a war correspondent for two decades, had reported from conflict zones across the Middle East and Africa.

Yukawa went to the region as he sought to reinvent himself as a soldier-of-fortune after a failed business career, a suicide attempt and the death of his wife, he wrote on his personal blog in April.

He returned to Syria in July and was captured by ISIS within weeks of his arrival. The group released a video in August showing a bloodied Yukawa being interrogated.

His capture prompted Goto, a devout Christian, to head to the northern Syrian city of Aleppo seeking his release, according to Kyodo news agency. Goto ended up a hostage facing the same death sentence, after leaving a video message in which he said his fate was his own responsibility.

Goto's mother told reporters on Friday that her son's wife recently gave birth to a child.

"America has known this pain and horror ourselves, and we stand with Japan not just in sadness, but in solidarity and strength," US Secretary of State John Kerry said in a statement.

"We grieve with Haruna Yukawa's family and loved ones, and with all the people of Japan."