AMMAN, Jordan — The Islamic State claimed to have beheaded a Japanese journalist in a video released Saturday night, the culmination of a two-week-long drama that appears to have cost the lives of two Japanese men.

The video of the killing of the journalist, Kenji Goto, came two days after a deadline set by the extremist group expired, and the Jordanian government did not give in to its demand that a convicted would-be suicide bomber be exchanged for Mr. Goto’s life.

Prime Minister Shinzo Abe, reacting to the release of the video, said Sunday that Japan would not give in to terrorism. President Obama issued a statement in which he said the United States “condemns the heinous murder” of Mr. Goto, whom he described as a courageous journalist.

Left unclear by the video, which was posted on a Twitter account associated with the Islamic State’s media organization, Al Furqan, was the fate of a Jordanian pilot, whom the extremists also threatened to kill if Jordan did not release the would-be bomber, Sajida al-Rishawi. Japan had not yet authenticated the video. Jordan did not publicly comment.