TOKYO (REUTERS, AFP) - Japanese Prime Minister Shinzo Abe on Sunday branded the apparent killing of a Japanese hostage by the Islamic State in Iraq and Syria (ISIS) as "outrageous and unforgivable" and demanded the immediate release of a second captive, amid growing global revulsion.

Abe also said a video claiming that Haruna Yukawa, 42, had been killed was highly credible.

"Considering the unbearable pain and sorrow that his family must be feeling, I am speechless," he said. "Such act of terrorism is outrageous and impermissible, it causes me nothing but strong indignation," he added. "I condemn it strongly and resolutely."

He called for the immediate release of the remaining Japanese captive, reporter Kenji Goto, 47.

"I again strongly demand the immediate release of Mr Kenji Goto unharmed."

"We are using every diplomatic channel and means to work towards a release," he told reporters in brief remarks after calling a meeting with his foreign, defence and other ministers after midnight in Tokyo.

The government will continue analysing the images to fully confirm the authenticity of the video, he added.

"We have been looking into its authenticity, but unfortunately at the moment we cannot help saying its credibility is high," he said on the public network NHK.

The father of Haruna Yukawa told the media of the horror of realising the threats to kill his son had been carried out.

"I went totally blank, I was only sorry... I had no words to say," Shoichi Yukawa said. "In my mind I wish very much that this wasn't true."

The nearly three-minute recording, posted online on Saturday, shows a still image of Goto holding an apparent photograph of Yukawa's slain body, with an audio recording in which Goto spoke of the ISIS group's demand for a prisoner exchange to guarantee his release.

It was not posted on any of the group's official channels and it does not bear their black and white flag. The purported execution of Yukawa is also not shown.

US President Barack Obama condemned the brutal murder of Yukawa in a statement released by the White House, which did not address how the United States had confirmed his killing. Earlier, US National Security Council deputy spokesman Patrick Ventrell had said the US intelligence community was working to verify the authenticity of the recording.

The Obama statement, issued while he was en route to India, said: "The United States strongly condemns the brutal murder of Japanese citizen Haruna Yukawa by the terrorist group ISIL," using an acronym to refer to Islamic State.

In a separate statement, US Secretary of State John Kerry also said Washington "strongly condemns the despicable murder of an innocent Japanese citizen, Haruna Yukawa."

The sudden escalation of the hostage crisis has become a test for Abe and the dominant news story in Japan since Tuesday when Islamic State militants released a video showing Goto and Yukawa kneeling with a knife-wielding, masked man demanding a US$200 million (S$270 million) ransom for their release.

The 72-hour deadline set in the first video expired on Friday.

Yukawa was seized by militants in August, after he went to Syria in what he described as a plan to launch a security company. Goto, a veteran war correspondent, went into Syria in late October seeking to secure Yukawa's release, according to friends and business associates.

The new recording, which was released on YouTube late on Saturday before being deleted, showed an image of a gaunt Goto in an orange t-shirt with audio of what appeared to be him making a statement in English.

In the apparent recording, Goto says Yukawa was "slaughtered in the land of the Islamic Caliphate."

But the journalist said the government of Japan could save him by working through Jordan where Abe set up an office earlier this week to coordinate the government's response to the hostage situation.

Goto says the militants would release him in exchange for the release of Al-Qaeda linked attempted female suicide bomber Sajida al-Rishawi, an Iraqi held in Jordan. He says the militants have dropped the ransom demand.

"I would like to stress how easy it is to save my life," the recording says. "You bring them their sister from the Jordanian regime, and I will be released immediately. Me for her."

Rishawi was arrested shortly after she failed to blow herself up in one of three deadly hotel bombings that hit the Jordanian capital in 2005.

Japanese officials have said little about how they were looking to secure the release of the captives over the past week.

In recent years, Japan has moved toward the US government's hard line against paying ransoms after a 1977 case in which it paid US$6 million to Japanese Red Army hijackers.

Finance Minister and Deputy Prime Minister Taro Aso said last week that responding to demands set by the Islamic State would mean "giving in to terrorism".

Japan's pacifist constitution also rules out any military response.

A briefing paper prepared for Abe's office on Friday and reviewed by Reuters said Japan would not have the legal authority to strike the ISIS even after proposed legislation loosening military restrictions the prime minister is seeking to pass later this year.

Abe and other officials have said Japan will press ahead with plans to offer over US$200 million in humanitarian aid to help deal with refugees displaced by ISIS.

Abe announced that aid a week ago in Cairo during a trip through the Middle East when he also called Islamic State a threat to the region and the international order.

The Islamic State has executed five British and American aid workers and journalists in recent months. Yukawa's capture by Islamic State fighters outside Aleppo in August was the first time a Japanese citizen has been held by the group.

Goto's mother, who had appeared before reporters on Friday in an emotional plea for his release, said she remained hopeful.

"The Japanese government will not let my son down. He will come back," Junko Ishido told reporters.