Islamic State (IS) militants said they had beheaded a second Japanese hostage, journalist Kenji Goto, and Prime Minister Shinzo Abe vowed never to forgive them "for this act."

The hardline Islamist group, which controls large parts of Syria and Iraq, released the video showing a hooded man standing over Goto with a knife to his throat, followed by footage of a head put on the back of a human body. Japanese Defense Minister Gen Nakatani said the video appeared to be genuine.

The video was released exactly a week after footage appearing to show the beheaded body of another Japanese hostage, Haruna Yukawa.

"I will never forgive these terrorists," Abe said. "Japan will work with the international community to bring those responsible for this crime to justice. Japan will never give in to terrorism."

"I feel intense indignation at this utterly cruel and despicable act of terrorism," a grim-faced Abe told an emergency Cabinet meeting early on Sunday, shortly after a video surfaced purporting to show the beheading of Goto, after the failure of international efforts to secure his release through a prisoner swap.

Japanese coalition and opposition politicians also expressed anger, but in a sign of a potential political split, the main opposition party questioned the wisdom of provoking IS.

"We must not appear to be giving in to terrorism," said Yukio Edano, secretary-general of the Democratic Party of Japan.

"But at the same time, putting our subjective intentions aside, there is no need to provoke and send a message that can be mistakenly interpreted as giving the other side an excuse," he said in a discussion program on public broadcaster NHK.

When IS first threatened Goto, 47, and Yukawa, 42, two weeks ago, it justified its move by citing Abe's pledge of $200 million in aid to countries battling the militant group.

In a show of defiance, Abe on Sunday vowed to increase Japan's food, medicine and other humanitarian aid for the Middle East.

IS had said Goto was held along with a Jordanian pilot. Efforts to win their release had focused on the possible release in exchange of an Iraqi would-be suicide bomber jailed in Jordan 10 years ago. The video did not mention the pilot.

Addressing Abe, the militant in the video said: "Because of your reckless decision to take part in an unwinnable war, this knife will not only slaughter Kenji, but will also carry on and cause carnage wherever your people are found. So let the nightmare for Japan begin."

The militant had the same British accent as the man featured in previous IS videos showing beheadings. Goto wore an orange jumpsuit like IS captives in past footage.

The landscape in the video showed a hill and land covered in scrub, and appeared different to the desert setting of previous videos.

Goto's mother Junko Ishido, who earlier had appealed for his safe release, said, "I am too upset to find the words to express myself. My son's last act was to go to Syria to help a fellow Japanese. So I want people to understand my son's kindness and courage."

Goto's older brother, Junichi Goto, said, "I had hoped to give thanks for his return alive. But, as his brother, this outcome is very regrettable."

The beheading is fanning calls to allow Japan's long-constrained military to conduct overseas rescue missions as part of Abe's push for a more muscular security posture.

Some advocates of legal changes to make rescues possible, however, say Japan's military faces big hurdles to acquiring the capacity to conduct such missions, while critics say sending troops overseas would just increase the risk.

President Barack Obama said the US condemned the "heinous murder" and would continue to work with allies to destroy the hardline Islamist group. Britain and France also condemned the killing.

IS has beheaded a number of Western journalists and aid workers, saying they were paying the price for their governments' fight against the group.

It has also killed many local people, through beheadings, stonings and shootings, accusing them of violating their hard-line interpretation of Islamic law.

There was no mention in the one-minute video of Jordanian pilot Muath al-Kasaesbeh who was seized by IS after his jet crashed in northeast Syria in December during a bombing mission against the militants.

An audio message that appeared to be from Goto earlier this week said Kasaesbeh would be killed if Jordan did not free Iraqi Sajida al-Rishawi, in jail for her role in a 2005 suicide bomb attack that killed 60 people in the Jordanian capital Amman.

Jordan said on Sunday it was still ready to hand over Rishawi in a swap deal if its captured pilot was released.

Jordan's security and military agencies were making constant checks to see whether the pilot was still alive, government spokesman Mohammad al-Momani said.