FBI Director Robert Mueller's confirmation that his agency is reading Miranda rights to certain terrorists captured and detained overseas at the Bagram military base in Afghanistan and other places has sparked an outcry among some Republican lawmakers.

Mueller told House members in a letter dated June 12 that the FBI Mirandizes detainees overseas on a "case by case" basis, saying that it has been done in just a "handful" of the 4,000 cases at Bagram.

While Justice Department officials, who acknowledged the practice earlier this month, say it is done to "preserve the quality of evidence obtained" and note that it began under the Bush administration, some are concerned that investigators and interrogators will miss out on valuable information if the practice continues.

Sen. John Cornyn, the top Republican on the immigration subcommittee, urged President Obama to reconsider the practice, arguing it will make America and the world less safe.

"I believe it unnecessarily undermines our ability to gain valuable intelligence from terrorist detainees who would rather talk to their lawyers than to U.S. interrogators," he said in a statement.

"And if this ill-conceived practice is allowed to continue, I fear we are headed down a slippery slope that could lead to dangerous scenarios where American soldiers and Marines are forced to pause and read would-be suicide bombers Miranda rights before detaining them," he added.

He added "regarding Miranda, there has been no policy change and no blanket instructions issued for FBI agents to Mirandize detainees overseas."

Michigan Rep. Mike Rogers, a senior Republican on the House Intelligence Committee, accused the Obama administration earlier this month of quietly ordering the FBI to start reading Miranda rights to the suspected terrorists.

Rogers, a former FBI special agent who served in the U.S. Army, made the accusation after returning from Afghanistan where he made a visit to Bagram Air Base. He said soldiers were frustrated that the Miranda rights -- the right to remain silent, the right to an attorney -- was impeding their ability to pursue intelligence on the battlefield.

The FBI's decision to provide Miranda warnings to terror suspects at Bagram continues to be a source of tension between the military and intelligence officials because soldiers must also Mirandize suspects to compensate for the lack of FBI agents there, a source told FOX News.

But Gen. David Petraeus, head of Central Command, said this month that members of the U.S. military were not reading rights to detainees.

"This is the FBI doing what the FBI does," he said. "So we are comfortable with this."

FOX News' Jennifer Griffin and Jim Angle contributed to this report.