TOKYO — Japan reacted with sorrow and outrage on Sunday to the posting by the Islamic State of a video purporting to show the grisly killing of the journalist Kenji Goto, bringing an end to a hostage standoff that has horrified this usually tranquil nation.

Gripped by anger and disbelief, Japan has so far shown support for the strong line taken by Prime Minister Shinzo Abe, who did not meet the hostage takers’ initial demands on Jan. 20 for a $200 million ransom, pledging not to yield to terrorism. Mr. Abe strongly condemned the murder claim made in the video released early Sunday, saying Japan “will cooperate with the international community and make the terrorists pay the price.”

“I’m outraged by the despicable terrorist act, and I will never forgive the terrorists,” Mr. Abe told reporters on Sunday at the prime minister’s office in Tokyo.

For now, the Japanese public seems to be united in grief and a desire to show support for Mr. Abe and other leaders. However, political analysts have said that as the shock wears off, there will be more questioning of how Mr. Abe’s government handled the crisis, which began with the appearance online of a video from the militant group threatening the lives of two Japanese hostages, Mr. Goto and Haruna Yukawa. In that first video, the group called the country’s pledge of $200 million to help shore up the government of Iraq and to assist refugees in Turkey, Syria and Lebanon a “foolish decision” and called for a ransom of the same amount.