HARARE, Zimbabwe — Two former allies of Zimbabwe’s recently ousted president, Robert Mugabe, were ordered held without bail on criminal charges on Monday, in cases that are being closely watched for how the new government will treat Mr. Mugabe’s closest associates.

Ignatius Chombo, the former finance minister, faces charges of fraud, abuse of office and violating an anticorruption law. Kudzanai Chipanga, the former head of the youth wing of the governing ZANU-PF party, is accused of communicating falsehoods and undermining public confidence in the Zimbabwe Defense Forces, after he insulted the military’s top commander, Gen. Constantino Chiwenga, at a news conference last month.

General Chiwenga played a central role in the military intervention that toppled Mr. Mugabe.

Mr. Chombo and Mr. Chipanga were among the first officials to be arrested after the military intervention that led to Mr. Mugabe’s resignation last week.

Mr. Mugabe was essentially toppled as part of a power struggle within ZANU-PF. At his inauguration on Friday, the new president, Emmerson Mnangagwa, whom Mr. Mugabe had fired as vice president during the power struggle, called on Zimbabwe’s citizens to remain peaceful and to desist from any form of “vengeful retribution.”