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“There are real civil liberties issues here,” Mr. Leiter said, noting that FBI cases generally are closed for good reasons. He asked if “we’re going to start getting local police to put … surveillance on” everyone who has been cleared by the FBI.

“Think of that in the domestic terrorism context,” he said, citing as an example “a guy who’s got a lot of guns” whose neighbors report him to FBI, who interview him and find he “just likes to shoot guns.”

“How long do you keep going back?” he said.

Mr. Giuliani argued that the occasional overreach is worthwhile.

“Do we want to err on the side of never making a mistake and possibly wrongly identifying someone as a terrorist, or do we want to err on the side of not having more bombings like Boston?” he said.

In Boston on Wednesday, Dzhokhar Tsarnaev, 19, pleaded not guilty to 30 federal charges, including using a weapon of mass destruction to kill, during a seven-minute court hearing — his first public appearance since being captured four days after the bombings.

He appeared in the heavily guarded, packed courtroom with his arm in a cast and his face swollen, with swelling around his left eye and cheek. After giving his plea to the 30 charges, he was led out of the courtroom in handcuffs, making a kissing gesture toward his family with his lips.

He could be eligible for the death penalty if prosecutors choose to pursue it.

⦁ This article is based in part on wire service reports.