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.”

But many inside and outside Zimbabwe are fearful that Mr. Mnangagwa will replicate, rather than undo, Mr. Mugabe’s strongman style of governance.

Mr. Mugabe, at 93 still widely seen as the father of the country, appears to be personally spared any retribution. Mr. Mugabe’s spokesman has said that the former president will remain in Zimbabwe, and there is a fairly widespread consensus that going after him would destabilize the country.

It is not known what, if anything, was promised to Mr. Mugabe and his unpopular wife, Grace, before he resigned last Tuesday just as impeachment proceedings were about to begin. Just as unclear is what might happen to his former associates who lost out in the power struggle.

On Monday, Mr. Mnangagwa dissolved Mr. Mugabe’s cabinet and named two allies to top positions, in what appeared to be an effort to reassure neighbors and investors. Patrick Chinamasa will be acting finance minister, and Simbarashe Mumbengegwi will be acting foreign minister.

But public attention in Harare, the capital, was more focused on the old guard, represented by Mr. Chombo and Mr. Chipanga.

In denying the men bail, a magistrate, Elisha Singano, said that releasing Mr. Chombo would “disturb the peace and cause a public outcry,” and said that both men posed a flight risk.

In addition, the government said the police were still building their case. An investigating officer, Onsimor Chikomba, said that Mr. Chombo, if released, could compromise witnesses who are cooperating with the government.

Lovemore Madhuku, a law lecturer at the University of Zimbabwe who is representing the men, said he would appeal the denial of bail.

“It is very disappointing,” Mr. Madhuku said. “The court appears to have a predetermined position.”

“There was no evidence that my clients would interfere with any witnesses or that they would abscond,” he continued. “I am sure there is a lot of interference coming from elsewhere. I am sure the military control has extended to the judiciary.”

Mr. Madhuku said his clients told the court that the military detained them for days before handing them over to the police.

Mr. Chombo and Mr. Chipanga belong to a faction of the ZANU-PF party called Generation 40, which is allied with Mr. Mugabe’s wife, and which jostled for control with Team Lacoste, Mr. Mnangagwa’s faction.

Rashweat Mukundu, former director at the Media Institute of Southern Africa in Zimbabwe, said he was worried that the two men’s rights to a fair trial were being infringed upon.

“The greatest threat to the two was being held incommunicado by the military and now that the legal process has begun we have to wait and see how the case proceeds,” he said. “It is important for the state that this matter is handled in a manner that does not indicate persecution as this will be a dent on the political transition underway in Zimbabwe.”

Several other former allies of Mr. Mugabe have not been heard from since the military intervention, prompting widespread speculation that they might have fled the country to avoid arrest.