The hostage crisis is the biggest diplomatic test for Japanese Prime Minister Shinzo Abe since he took office in 2012 pledging to bolster Japan's defence and play a bigger role in global security.
Speaking after a special cabinet ministers' meeting as well as in parliament on Thursday, Abe said the government was making every effort to ensure Goto's early release and repeated that Japan was seeking cooperation from Jordan.
He reiterated that Japan would not give in to terrorism and that Tokyo would keep cooperating with the international community. He added that Japan would make every effort to protect its citizens at home and abroad from terrorism.
"If we are too afraid of terrorism and give in to it, this will give rise to fresh terrorism against Japanese and it will become a world in which the will to carry out despicable violence has its own way," Abe told a lower house budget committee. "Such a thing is totally impermissible."
The hostage crisis erupted after Abe, while on a tour of the Middle East, announced $200 million in non-military aid for countries contending with Islamic State, but his government has rejected any suggestion it acted rashly and stressed the assistance was humanitarian.
Abe added that peace and stability of the Middle East were important for Japan's energy strategy. Resource-poor Japan relies heavily on the Middle East for oil imports.
Goto went to Syria in late October. According to friends and business associates, he was attempting to secure the release of Haruna Yukawa, his friend and fellow Japanese citizen who was captured by Islamic State in August.
In the first of three videos purportedly of Goto, released last week, a black-clad masked figure with a knife said Goto and Yukawa would be killed within 72 hours if Japan did not pay Islamic State $200 million.
A video on Saturday appeared to show Goto with a picture of a decapitated Yukawa, saying his captors' demands had switched to the release of al-Rishawi.
Tuesday's video featured an audio track over a still picture that appeared to show Goto holding a picture of a now bearded Kasaesbeh.