By Martin Finucane Globe Staff

A federal judge has denied a request by embattled former state probation commissioner John J. O’Brien for the appointment of two particular lawyers to represent him, but left the door open to appointing others to represent O’Brien at the government’s expense.

US District Judge Timothy Hillman said O’Brien, if he turns out to be eligible, must instead use federal public defenders or someone from a list of private attorneys who do court-appointed federal defense work.

Hillman rejected O’Brien’s request to approve funding for Paul Flavin, his long-time lawyer who has already represented him in state criminal investigations and in state hearings, and Anthony M. Traini of Providence, whom Flavin wanted on his team because of his expertise in federal white-collar crime cases.

“I understand and appreciate that these charges are life altering and exceptional to O’Brien and his family, but under the present circumstances, I cannot find that exceptional circumstances exist which warrant” the government paying for the lawyers specifically requested by O’Brien, the judge said.

O’Brien and two other people are charged with racketeering conspiracy, racketeering, and mail fraud. They allegedly ran a rigged hiring and promotional system that rewarded those with political connections.

While denying the request for funding for Flavin and Traini, Hillman noted that “if O’Brien wishes to make application for court appointed counsel, I would entertain that application.” But the judge said he hadn’t yet completed his analysis of whether O’Brien is eligible for a government-paid defense lawyer.

Under the federal Criminal Justice Act, criminal defendants in federal court in Massachusetts who don’t have the means can get representation from either the federal public defender office or private attorneys who have volunteered to serve on the CJA Panel.