BAGHDAD — Iraq’s Supreme Court will oversee a manual recount of ballots from last month’s election, according to an announcement Thursday, as a crescendo of fraud complaints and criticism of the country’s electoral commission threatened to undermine the legitimacy of the tightly contested vote.

The announcement from the court came in response to an unusual and politically tinged vote in Parliament on Wednesday in which lawmakers amended the election law to demand a manual recount overseen by a panel of judges.

The May 12 election appeared to result in a surprising victory for the coalition led by Shi’ite cleric Muqtada al-Sadr.

Since the election result, politicians have made a barrage of complaints about voting irregularities, and have made competing demands to address those flaws. The vote and its aftermath have crystallized pent-up frustration among Iraqi political parties and the international community about the performance of the Independent High Electoral Commission of Iraq, the agency that oversees elections.

NEW YORK TIMES