As a sunset cutoff for a prisoner exchange on the Turkish- Syrian border loomed, the wife, who signed her name only "Rinko," said she was begging Tokyo and Amman to save the lives of her husband and a Jordanian pilot.
Islamic State militants say they will kill the airman unless Jordan frees failed Iraqi suicide bomber Sajida al-Rishawi in exchange for Goto.
"In the past 20 hours the kidnappers have sent me what appears to be their latest and final demand," Rinko said in a statement published on the website of the Rory Peck Trust, an organisation that supports freelance journalists.
In their latest message, IS -- which rules large swathes of Iraq and Syria under an extreme version of Islamic law -- said they were willing to free Goto, a respected war reporter.
But Jordan is demanding the return of pilot Maaz al-Kassasbeh, whose F16 fighter jet crashed over northern Syria on December 24.
With the militants' deadline looming, Jordan said it was still waiting to see evidence that Kassasbeh was still alive -- something the group has so far refused to offer.
"Our baby girl was only three weeks old when Kenji left. I hope our oldest daughter, who is just two, will get to see her father again. I want them both to grow up knowing their father," she said.
"My husband is a good and honest man who went to Syria to show the plight of those who suffer.
"I fear that this is the last chance for my husband and we now have only a few hours left to secure his release and the life of (Maaz al-Kassasbeh).
"I beg the Jordanian and Japanese government to understand that the fates of both men are in their hands.
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