Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, suggested Sunday that the United States could do more to fight terrorism but predicted eventual defeat for the new-but-extremely-violent Islamic State group.

Dempsey told “Fox News Sunday” that defeating terrorism will require an increased group effort that includes the U.S. military and intelligence community.

“But that does not imply we're not doing enough,” he said.

In an exclusive and wide-ranging interview, Dempsey also gave his support for closing the U.S. prison in Guantanamo Bay, Cuba, saying the facility, opened in the aftermath of the 9/11 terror attacks, is a “psychological scar” on the American psyche.

“It’s in the national interest to close Guantanamo,” he said.

President Obama vowed during his first presidential campaign, in 2008, to close the facility. He continues to release detainees to the point where the facility has only a few dozen people left. Nearly 800 have passed through Guantanamo since it opened in 2002.

Dempsey said about a dozen of them “simply will not be released” but declined to comment on what the U.S. should do with them.

“Now isn’t that an interesting decision for elected officials?” he said.

Dempsey argued that Islamic State, which has over roughly the past year gained prominence and strength in Iraq and Syria, particularly for its videotaped beheadings of several Westerners, will collapse under its own power. He said the group’s violent nature will prove to be an unsustainable existence for members.

He also said the U.S. military has the capability to attack the Syrian regime led by President Bashar al-Assad should Obama give the orders.  

“Of course we could,” Dempsey said.

He avoided disagreeing with Obama, who in late December, marking the end of the U.S. military’s official combat mission in Afghanistan, said that country would no longer be “a source of terrorist attacks again.”

Dempsey said: “There will be pockets of that country that change hands from time to time. But we’re going to have to keep an eye on them. … I tend to be a little paranoid.  … Terrorism flows where instability lurks.”