Three men accused of participating in what prosecutors have called one of the most audacious contracting scams in U.S. history on Thursday were ordered held in jail until their trials.

A fourth defendant will remain detained until another court proceeding next week, the federal judge said.

The four men — two program managers with the Army Corps of Engineers, a son of one of them and the contracting director of a Dulles-based firm — were arrested Tuesday and accused of stealing about $20 million in a long-running kickback scheme.

The two Corps employees — Kerry F. Khan, 53, of Alexandria, and Michael A. Alexander, 55, of Woodbridge — Khan’s 30-year-old son, Lee, and contracting director Harold F. Babb, 60, were charged with conspiring to commit bribery, money laundering and wire fraud. All four have pleaded not guilty.

At a Thursday hearing in the District’s federal court, Magistrate Judge Deborah A. Robinson ordered Lee Khan and Alexander held without bond; Kerry Khan consented to detention.

Babb will be held ahead of a hearing, scheduled for Tuesday, because his attorney, Jeffrey Jacobovitz, requested more time to prepare. After the hearing, Jacobovitz said it was “important to remember” that the charges represent “one side of the story.”

Assistant U.S. Attorney Michael Atkinson argued in court and in filings that the men should be detained because they might flee in the face of “overwhelming” evidence that includes secretly recorded conversations and meetings and because they face the potential for stiff prison terms if convicted.

Atkinson said the men also have international connections and access to cash that might make it easier to run.

When investigators searched Alexander’s house Tuesday, Atkinson said, they found $180,000 in cash in a bedroom drawer. “Alexander is personally responsible for executing a covert scheme of deceit, where he was paid or promised in excess of $1 million in bribes,” Atkinson wrote in court papers.

Atkinson said that Lee Khan was too dangerous to release because he had already threatened a potential government witness: his own brother.

Atkinson said that the brother, in jail on an unrelated drug charge, had threatened to tell authorities about the scam unless he received money. The brother eventually was paid about $400,000 to keep quiet, Atkinson said. But Lee Khan still was worried that his brother might help investigators.

“If anything like that happens, you are losing a son because I will kill that [expletive] myself,” Lee Khan told his father, Kerry Khan, according to court papers filed by prosecutors. “That’s all there is to it. . . . If I have to find somebody locked up to [expletive] shank him, he’s going down.”

Edward Sussman, Lee Khan’s attorney, argued that his client should be released pending trial and countered that the inflammatory statements might have been made in the heat of the moment. Lee Khan has a 12-year-old daughter, doesn’t travel internationally and served in the U.S. military, Sussman said.

Alexander’s attorney, Christopher Davis, urged Robinson to release his client because his wife is battling cancer and has no one else to care for her. “She needs him,” Davis said.

Davis called the allegations a mere “snapshot” in a life of “public service” and said his client would not flee if released.

In siding with prosecutors, Robinson said she could not see any conditions of release that would “reasonably assure” her that Alexander and the younger Khan would return to court and added that Lee Khan posed a safety risk to the community.

Prosecutors say the four men worked out a sophisticated scam, which started in 2007 and lasted until their arrests, that targeted certain contracts at the Army Corps. Babb worked for EyakTek, a company with offices in Dulles and Anchorage that could take advantage of its status as an Alaskan native-owned corporation to obtain contracts of unlimited size without competition.

Babb, Khan and Alexander then ensured that a subcontractor, identified in court papers as “Company A,” got work to perform information technology services, prosecutors said. Company A’s chief technology officer, or “Co-Conspirator 1” in the indictment, then submitted inflated invoices to the Army Corps or through EyakTek.