U.S. Sen. Ted Cruz on Friday pushed back against claims that it was insensitive for him to hold a Second Amendment campaign event just days after a mass shooting under investigation as an act of terrorism.

"I really don't view our job as being sensitive to Islamic terrorists," the Republican presidential candidates said at a gun range in Johnston, Iowa, where he rolled out his Second Amendment Coalition, a group of gun rights advocates backing his GOP presidential bid.

"Liberal Democrats think it is insensitive to celebrate our constitutional rights in the wake of a terrorist attack," Cruz later told supporters. "It is these constitutional rights that keep us safe."

The event at Crossroads Shooting Sports came two days after a shooting in San Bernardino, California, left 14 people dead and 21 wounded. The FBI said Friday it was looking into the massacre as an act of terrorism, potentially with a connection to the Islamic State terrorist group. Cruz regularly blasts President Barack Obama for not taking the group seriously enough.

Texas' junior senator also routinely rips Obama for advocating increased gun control in the aftermath of mass shootings, but his remarks Friday were sharper and more extensive than usual.

Earlier Friday, Democrats criticized Cruz's shooting range appearance as tone deaf in light of the California massacre. They noted that a number of Republican senators, including Cruz, put themselves on the record against gun control measures as recently as Thursday night in Washington, D.C.

"It’s been one day since Ted Cruz voted against preventing people on a federal terrorism watch list from purchasing guns, and only two days since San Bernardino, yet Cruz and the GOP are doubling down against gun control,” Adrienne Watson, a spokesman for the pro-Hillary Clinton super PAC Correct the Record, said in a statement. "Though it’s irresponsible, it’s no surprise. But a shooting range? If we’re rewarding insensitivity, Ted Cruz takes the cake."

Cruz said the Second Amendment Coalition, a group of more than 24,000 gun rights advocates, includes more than 1,000 members in the first four early voting states. The coalition has five co-chairs: Tim Macy, president of Gun Owners of America; Bob Barr, a former U.S. representative from Georgia; Sgt. Patrick Perkins, president and co-founder of Heroes Hunting; Richard Rogers, a member of the Iowa Firearms Coalition board; and Dave Funk, a GOP activist from Iowa.