A defiant Abe vowed he would not bow to "terrorism" as Japan was thrust abruptly into the conflict gripping Syria and Iraq, where jihadists have seized control of large areas.
"I strongly demand that they not be harmed and that they be immediately released," he told a news conference in Jerusalem.
"The international community will not give in to terrorism and we have to make sure that we work together."
In footage posted on jihadist websites, a black-clad militant brandishing a knife addresses the camera in English, standing between two hostages wearing orange jumpsuits.
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"You now have 72 hours to pressure your government into making a wise decision by paying the USD 200 million to save the lives of your citizens," he says.
The militant says that the ransom sum is equal to the aid that Abe pledged in support of the fight against IS.
Supportive voices came from around the world, with US Secretary of State John Kerry telling his Japanese counterpart Fumio Kishida that Washington stood firmly behind Tokyo.
Japan, a constitutionally pacifist country has steered clear of the armed entanglements of the US, Britain and other Western nations in the Middle East.
The ensnarement of two of its citizens in the IS group's bloody ideological battle is deeply shocking to Japan, and there is likely to be considerable domestic pressure on Abe to try to negotiate their release.