The postponement exacerbates Iraq's political problems because it is the task of the president to formally name a prime minister, who must be backed by an absolute majority in parliament.
The Supreme Court's decision came after Iraqi MPs submitted a complaint against initially favourite presidential candidate Hoshyar Zebari based on corruption charges.
Only 58 members out of 329 lawmakers were present in the parliament, which was less than the necessary two-thirds quorum needed to choose a new president for the mostly ceremonial post.
Iraq's largest bloc in parliament has announced that it will not attend Monday's session to elect the president, making a vote unlikely.
With thousands of people killed and a million displaced, entire neighbourhoods are ravaged and survivors are in dire need of aid.
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