The hostages are identified in the video as Kenji Goto Jogo and Haruna Yukawa.
The Japanese Prime Minister Shinzo Abe, who was speaking from Jerusalem, demanded Isis release the two men immediately.
Mr Abe had on Saturday pledged $2.5bn in non-military assistance to the Middle East. He also promised $200m in non-military aid for countries tackling Isis.
Speaking in English and with a British accent, the militant says: “To the prime minister of Japan: Although you are more than 8,000 and 500 kilometers (5,280 miles) from Isis, you willingly have volunteered to take part in this crusade.
“You have proudly donated $100m (£66m) to kill our women and children, to destroy the homes of the Muslims.”
The militant warns the Japanese public had 72 hours to pressure their government to stop its “foolish” support for the US-led coalition waging a military campaign against Islamic State.
“Otherwise this knife will become your nightmare,” the black-clad figure said in English. He demanded “200 million” without specifying a currency, but an Arabic subtitle identified it as US dollars.
Goto is a freelance reporter who was based in Tokyo. He has written books on AIDS and children in war zones from Afghanistan to Africa and reported for news broadcasters in Japan.
Goto met Yukawa last year and helped him travel to Iraq in June, he told Reuters in August.