Japan’s prime minister, Shinzo Abe, has vowed his country will continue to play an active and constructive role abroad, undeterred by the execution of a Japanese security contractor by Islamic State extremists.

The apparent beheading of Haruna Yukawa has shocked Japan and intensified anxiety over the fate of another hostage, Kenji Goto, a freelance journalist. However, there is little consensus on how to respond.

Some have argued that the hostages acted irresponsibly, pointing to the fact that both travelled to Syria independently and at great risk. But there have also been murmurs of discontent directed at Abe and his advocacy of an assertive and outgoing foreign policy.

Isis had initially demanded $200m (£135m) for the release of Yukawa and Goto, linking the ransom to Japanese aid to support refugees in the region. Following Yukawa’s murder, Isis has dropped its ransom and demanded the release of a female jihadist held in a Jordanian jail for a 2005 attempted suicide bomb attack.

Abe said on Sunday that Japan would not be deflected from its foreign mission. “We will never give in to terrorism, and we will actively contribute to the peace and stability of the world together with the international community. We are not wavering at all on this policy,” the prime minister said.

Since his reelection in December, Abe has supported proposals to remove article 9 of Japan’s constitution, adopted after the second world war and drafted by US occupation forces, which renounces the use of war or the threat of force to resolve international disputes and bans the maintenance of armed forces with “war potential”.

His government has already loosened the conditions in which Japan’s Self-Defence Forces can be used, to include the protection of close allies. But there is limited public support for such changes, and it is far from clear whether the impact of the hostage trauma will strengthen Abe’s hand or intensify calls for Japan to withdraw from its foreign policy commitments on the far side of the world.

Abe said the murder of Yukawa, 42, was “outrageous and unforgivable” and called for the release of 47-year-old Goto.

Japanese and US analysts have said they have no reason to doubt the authenticity of a video published online in which Goto, in shackles, holds a photograph that seems to show Yukawa’s body after his beheading.

In a audio message released with the photograph, a voice purporting to be Goto’s asks for the release of Sajida Mubarak al-Rishawi, an Iraqi jihadist whose suicide belt failed to detonate during an attack on three hotels in the Jordanian capital, Amman, in 2005.

“They no longer want money,” the voice says in accented English. “You bring them their sister from the Jordanian regime, and I will be released immediately. Me for her. Don’t let these be my last words you ever hear. Don’t let Abe also kill me.”