The widening inquiry has unfolded over several days and has quickly become a political crisis for Mr. Erdogan, perhaps the worst he has faced in more than a decade in power. Commentators and government officials have linked the investigation to a popular imam who lives in Pennsylvania, Fethullah Gulen, whose followers are said to have taken up high-level positions in the Turkish police and judiciary over the years.

Mr. Erdogan and Mr. Gulen, who represent different Islamic traditions in Turkey, were once allies, and they teamed up to push the military from politics through a series of trials that landed a number of generals and officers in prison in recent years.

Mr. Gulen, who rarely speaks to the news media, denied any involvement in the corruption case in a statement released by his lawyer last week. On Saturday, though, he released an emotionally charged video in which he appeared to denounce the government’s efforts against his supporters, raising the stakes in what has become an epic fight between the two former partners.

At times he waved his arms and in impassioned language said, “May those who don’t see the thief but go after those trying to catch the thief, who don’t see the murder but try to defame others by accusing innocent people — let God bring fire to their houses, ruin their homes, break their unities.”

Mr. Erdogan has simultaneously blamed foreigners — as he did during mass protests in the summer against what opponents called his government’s heavy-handed efforts to raze a park — and begun a purge of the police forces, removing dozens of officials said to be involved in the corruption investigation.

The inquiry has led to the detentions of dozens of businessmen and officials, as well as the sons of three cabinet ministers. On Saturday, the general manager of Halkbank, the sons of the interior and economy ministers, and 13 others were formally arrested in the case.