Defense Secretary: U.S. military goal is 'degrade and destroy' ISIS -- not containment

(CNN) -- America's top defense official says the goal of the United States is to "degrade and destroy" the capabilities of ISIS fighters in Iraq and Syria, not contain them.

The statement by Defense Secretary Chuck Hagel came during an interview with CNN's Jim Sciutto on Wednesday, just hours after President Barack Obama said the United States will not be intimidated by the killers of two American journalists.

"Those who make the mistake of harming Americans will learn that we will not forget ... that our reach is long and that justice will be served," the president said.

Obama's words followed the U.S. authentication Wednesday of an ISIS terror group video, released the day before, showing the beheading of journalist Steven Sotloff.

Sotloff's family broke their silence Wednesday, describing the journalist who was abducted in August 2013 as a man who "merely wanted to give voice to those who had none."

"Their story was Steve's story. He ultimately sacrificed his life to bring their story to the world. Steve was no hero. Like all of us, he was a mere man who tried to find good in a world of darkness, and if it did not exist, he tried to create it," according to a statement read by family spokesman Barak Barfi.

"...Today, we grieve. This week, we mourn. But we will emerge from this ordeal ... We will not allow our enemies to hold us hostage with the sole weapons they possess, fear."

The killing is the second beheading of an American journalist in two weeks, and the militant group said it's a result of Obama's decision to conduct airstrikes in Iraq against ISIS, which also calls itself the "Islamic State."

"It makes you sick to your stomach, but it again reminds you of the brutality and barbarism that is afoot in some places in the world," Hagel said. "...It won't just recede into the gray recesses of history until we stop it."

Hagel: All options on the table

All options -- with the exception of a ground invasion -- are on the table to address the threat posed by ISIS, Hagel said.

Those options include possible airstrikes in Syria, where ISIS has established a stronghold in and around the northeastern Syrian city of Raqqa.

Vice President Joe Biden added his own voice to the calls for justice, saying the United States will pursue the killers "to the gates of hell."

"As a nation, we are united, and when people harm Americans, we don't retreat, we don't forget," he said at an appearance near Portsmouth, New Hampshire.

"We take care of those who are grieving. And when that's finished, they should know we will follow them to the gates of hell until they are brought to justice, because hell is where they will reside. Hell is where they will reside."

'A punch to the gut'

In a scene eerily similar to an earlier video of the death of U.S journalist James Foley, Sotloff kneels in the desert, dressed in an orange prison-style jumpsuit. A masked "executioner" lords over him, wielding a knife.

"I'm back, Obama, and I'm back because of your arrogant foreign policy towards the Islamic State," the executioner says. "Just as your missiles continue to strike our people, our knife will continue to strike the necks of your people."

U.S. Secretary of State John Kerry said the latest video shows ISIS' "unfathomable brutality."