BAGHDAD—Iraq's Shiite Prime Minister Nouri al-Maliki warned that a challenge to his government by Sunni politicians could destroy the ethnic and sectarian power-sharing system that underpins Iraq's democracy—and take more power into the hands of the Shiite majority.

The threat signals the most dire political crisis Iraq has faced since an agreement on a governing coalition one year ago smoothed over a long-running conflict that has re-emerged with the official pullout this month of U.S. forces from Iraq.

The...