Maryland court are being held to determine whether Bradley, 24, should be tried on charges of steeling secret US cables and passing them over to WikiLeaks which could send him to jail for the rest of his life.
Defence lawyers said that because the reserve officer overseeing the hearing, Lt Col Paul Almanza, who is known in the military as the investigating officer, has a day job at the Department of Justice, he cannot be impartial, ABC News reported.
The Justice Department is also investigating Manning, who made his first court appearance yesterday after more than a year-and-a-half of detention.
But Almanza denied the defence attorneys' request and said he would not recuse himself because a reasonable person would believe he could remain unbiased.
Earlier, Almanza asked Manning procedural questions like whether he had a copy of the charges against him.
"Yes, sir, I do," Manning replied.
Asked whether he had any questions, the accused replied, "No, sir."
To another question as to whether he was comfortable with his legal counsel, Manning said, "Yes, sir."
Manning, who wore his camouflage uniform and sported thick black-rimmed glasses during the hearing, is accused of downloading 260,000 US diplomatic cables, videos of American air strikes and US military reports from Afghanistan and Iraq between November 2009 and May 2010 while serving in Iraq and giving them to WikiLeaks. He was arrested on May 26, 2010.