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“There is no doubt the president has the right to review all of the practices used at Guantanamo to determine which ones are acceptable and which ones are not, but he should not close the facility,” said Mr. Coffman, who served two tours of duty in Iraq.

Indeed, organizers of the petition said they hoped the drive would lead to a national discussion on whether the Cuba-based facility should be closed.

“This is really a first step,” Mr. Gardner said. “Across the nation, Democrats and Republicans alike are saying ‘no’ to terrorists in their state. I’m receiving e-mails from people saying we need to circulate a public petition that would send a strong message to President Obama on keeping the base open.”