Both teams of foreign observers faulted the last-minute addition of a third day as a needless irregularity that raised doubts about the credibility of the process and the independence of the election authorities.

Mr. Bjornlund of Democracy International said his observers had seen no impediments to voting on the first two days that might have justified a third day, and the European Union delegation said the third day “caused unnecessary uncertainty in the electoral process.”

Egyptian officials said supervision of the government’s High Presidential Election Commission, composed of senior judges, was politically independent and assured the integrity of the vote. But in previous Egyptian elections the best checks on fraud were parallel counts by independent political groups — principally the Muslim Brotherhood — as well as the close monitoring of representatives of opposing campaigns.

Now, the Brotherhood, which dominated Egyptian elections through its political arm over the previous three years, has been outlawed and repressed. On the night before the added day of voting, the Sabahi campaign withdrew its monitors from the polls, complaining that security forces there were excluding, assaulting and arresting them.

As a result, Mr. Bjornlund said, the turnout or vote count could not be confirmed by the relatively small observer missions.

“We do not know what the turnout for this election was,” he said. Democracy International’s 86 monitoring teams did not see a large turnout, he said, but the group “has no means to evaluate it.”

At least one judge on the election commission has publicly questioned some fundamental tenets of democracy. In the run-up to Egypt’s first parliamentary elections after the ouster of President Hosni Mubarak in 2011, the judge, Nabil Salib, argued in a newspaper column that democratic elections were unsuitable for Egypt because so many Egyptians were poor and uneducated.

“I argue for canceling elections” until “illiteracy vanishes, citizens’ living conditions are secured at least to a minimum standard, their will is liberated and their culture is sophisticated,” he wrote, recommending that a committee of judges and intellectuals choose the leaders. “Canceling elections is the beginning of the real road to reform and the first correct step in the thousand miles path.”