The Islamic State group said on Thursday on its affiliated radio station that its Egyptian branch has killed the Croatian hostage.
This news comes a day after a photo purporting to show the captive's headless body circulated online.
In an audio broadcast of its Al-Bayan station the group said, "the soldiers of the Caliphate killed the Croatian captive whose country is participating in the war on the Islamic State."
It said the slaying came after a 48-hour ultimatum, given to Egypt to free Muslim women prisoners, expired and both the "apostate Egyptian government and his own have abandoned him."
Egypt's Foreign Ministry said authorities have not had "confirmed information" about the murder, and the Croatian Prime Minister Zoran Milanovic said he could not confirm it "with certainty."
Foreign Minister Sameh Shoukri told his Croatian counterpart Vesna Pusic by phone on Wednesday that the authorities were trying their utmost to catch the kidnappers.
The picture, posted Wednesday on Twitter accounts affiliated with the Sinai Province group, purported to show the decapitated corpse of Tomislav Salopek with his head placed on his back and the signature black flag of IS group planted in the sand nearby.
Egypt has been fighting an increasing Islamist insurgency in North Sinai that is spearheaded by Sinai Province group, the country's most lethal militant faction.
Although the group has killed hundreds of police officers and military personnel, foreigners have largely been spared from the violence.