ANKARA, Turkey — The credibility of the judges who oversaw Turkey’s referendum last week is being called into question because most of them were hastily appointed when President Recep Tayyip Erdogan purged the judiciary after last summer’s failed coup.

A narrow majority of Turks voted on April 16 to change the Constitution in a poll that formally granted vast new powers to the office of the Turkish presidency beginning in 2019 and informally validated the already-authoritarian mind-set of Mr. Erdogan.

But the legitimacy of Mr. Erdogan’s victory has been tainted by accusations of voter fraud at polling stations across the country — and by an odd series of erratic decisions on the day of the vote by the judges who head the electoral commission. Eight of the 11 judges on the panel had been recently replaced.

The opposition has questioned the results of thousands of ballot boxes, after videos showed evidence of ballot-box stuffing and voter intimidation on the day of the vote, and opposition campaigners faced prolonged intimidation during the campaign that preceded it.