 An earlier tape showed Mr Kim pleading for his life |
The body of translator Kim Sun-il, 33, had been found, the foreign ministry said. The al-Jazeera TV station reported that he was beheaded.
Mr Kim was working for a security company supplying the US military when he was abducted last week near Falluja.
South Korea rejected demands that it end its military role in Iraq in return for Mr Kim's life.
 |  This is what your hands have committed - your army has not come here for the sake of Iraqis, but for cursed America  Militants' statement |
Arabic satellite channel al-Jazeera said it had received a new video tape saying that Mr Kim had been killed by a group identifying itself as Jamaat al-Tawhid and Jihad.
Last month, the same group - led by a top al-Qaeda member, Abu Musab al-Zarqawi - beheaded American hostage Nick Berg. It has also been responsible for a number of other attacks, including the killing of Iraqi Governing Council head Ezzedine Salim.
In the latest footage aired on al-Jazeera, Mr Kim was shown kneeling on the ground in front of five masked men.
His shoulders were heaving, his mouth open. He wore a bright orange jumpsuit and matching blindfold.
The part of the tape broadcast did not show him dead, but the presenter said Mr Kim had been beheaded.
One of the masked kidnappers read a statement addressed to the Korean people, saying: "This is what your hands have committed. Your army has not come here for the sake of Iraqis, but for cursed America."
'I don't want to die'
Seoul earlier insisted it would go ahead with plans to deploy 3,000 troops to northern Iraq, to add to a force of 600 already in the country.
A previously released two-minute tape of Mr Kim begging for his life - first shown on al-Jazeera on Sunday - has seared itself into the consciousness of South Korea, our correspondents say.
Mr Kim was seen screaming: "Korean soldiers, please get out of here. I don't want to die. My life is important."
Hundreds of ordinary South Koreans e-mailed al-Jazeera trying to convey appeals for mercy to the militants.
The video showed the hostage surrounded by armed men wearing masks.
