Allen said there is an element of cross-border criminal activity that needs to be addressed, but that makes up just 5 percent of illegals crossing the border.

"Fanning the flames of fear and insecurity across the country by inflating the realities here simply won’t result in good policy, just in good campaign speeches," Allen said.

Flake had just returned from a tour of Arizona border areas in Douglas, Nogales and Yuma along with Arizona GOP Sen. John McCainJohn Sidney McCainRubio asks Army to kick out West Point grad with pro-communist posts The VA's woes cannot be pinned on any singular administration Overnight Defense: Mattis offers support for Iran deal | McCain blocks nominees over Afghanistan strategy | Trump, Tillerson spilt raises new questions about N. Korea policy MORE and Republican Reps. David SchweikertDavid SchweikertDeficit hawks voice worry over direction of tax plan FreedomWorks: Tax reform failure could be 'end of GOP as we know it' Freedom Caucus backs three debt ceiling options MORE, Paul GosarPaul GosarHouse conservatives: Rove's criticism 'wrong and misguided' House votes to block funding for EPA methane pollution rule McCain needs to start showing my constituents more respect MORE and Ben Quayle. The tour included a meeting with the widow and brother of Robert Krentz, a rancher slain last year near the border.

Flake is vying for the Republican nomination to seek the seat being vacated by Sen. Jon Kyl (R-Ariz.), who is retiring in 2012.