Minas Ibrahim al-Yusufi, the secretary-general of Iraq's Christian Democratic Party, was seized from the northern city of Mosul on 28 January.
His captors have threatened to behead him if they do not receive a ransom for his release.
"I appeal to King Carl XVI Gustaf, Queen Silvia, Pope John Paul II, the international union of Christian parties and the Association of Muslim Scholars … to work for my release and enable me to complete my national mission," he said.
Al-Yusufi was seen in the video aired by an Arab television channel sitting in front of a black banner bearing the name of the Iraqi Vengeance Brigades.
He had called his family in Sweden on 6 February, saying he was being held by 15 armed men.