ɪn tˈuː θˈaʊzənd fˈaɪv, ˈældʒˈuːbɛɹi wʌz bˈækt baɪ ðə sˈʌni ˈæɹəb dˈaɪəlɑːɡ kˈaʊnsəl æz ðɛɹ kˈændᵻdˌeɪt fɔːɹ spˈiːkɚɹ ʌvðɪ ɪɹˈæki nˈæʃənəl ɐsˈɛmbli, bˌʌt hiː wʌz vˈiːɾoʊd baɪ ðə juːnˈaɪɾᵻd ɪɹˈæki ɐlˈaɪəns dˈuː tə hɪz lˈɪŋks wɪð jˈuːdeɪ hˈʌsiːn.
In 2005, al-Juburi was backed by the Sunni Arab dialogue council as their candidate for speaker of the Iraqi National Assembly, but he was vetoed by the United Iraqi Alliance due to his links with Uday Hussein.