WASHINGTON (CNN) -

President Barack Obama flatly stated Tuesday the United States won't forget the gruesome killing of American journalist James Foley and promised "justice will be done."

And now, apparently, he has some options to pursue such justice -- going after ISIS not just for beheading Foley, but for its campaign of terror around the region.

The U.S. Defense Department has given Obama "a range of planning options" to go after the Islamist terror group, State Department spokeswoman Marie Harf told CNN's Wolf Blitzer on Tuesday. That includes continuing to strike the group, as U.S. forces have done for weeks, inside Iraq as well as taking the fight into Syria.

"We're having a constant conversation inside the administration about what options could be necessary to go after ISIS whether it's in Syria, Iraq or wherever they train or operate," the spokeswoman said.

Harf added that the President -- who has authorized reconnaissance flights over Syria, according to a U.S. official -- hasn't made any decisions on what to do next. But, even if he hasn't offered specifics, he hasn't backed down in his rhetoric.

Speaking at an American Legion event Tuesday about Foley's killing -- which ISIS videotaped then put online as it threatened more such killings targeting Americans -- Obama said that, while his government will be patient, it also won't hesitate to use its vast reach to bring "justice" by going "after those who harm Americans" and others.

"We'll continue to take direct action where needed to protect our people and to defend our homeland," the President said in Charlotte, North Carolina.

"And rooting out a cancer like (ISIS) won't be easy, and it won't be quick. But tyrants and murderers before them should recognize that kind of hateful vision ultimately is no match for the strength and hopes of people who stand together for the security and dignity and freedom that is the birthright of every human being."

Official: U.S. won't coordinate with al-Assad

U.S. officials take pains to point out that they are going after ISIS already.

Militarily, that means increasing its presence in the Persian Gulf, boosting intelligence gathering and cooperation in Iraq, doing more for Iraqi security forces and conducting airstrikes in Iraq, Pentagon spokesman Rear Adm. John Kirby said Tuesday.

Still, if the United States is serious about going after ISIS -- wherever it is -- it can't count on the group to stay on the Iraqi side of the porous Syrian border. That's why striking in Syria is a possibility.

If that's what happens, it would mean Obama would be on the same side as Syrian President Bashar al-Assad -- the same man who U.S. officials have been railing at for years, going so far as to work closely with the "moderate opposition" forces trying to unseat him the past three years.

Yet these "moderate" forces aren't alone in trying to topple al-Assad. They've been joined by -- and sometimes fight against -- ISIS and other groups such as al-Nusra Front, that Washington calls terrorist organizations.

Syrian Foreign Minister Walid Moallem said al-Assad's regime was ready to accept support from the United States and others working under the U.N. umbrella to fight "terrorists" -- a reference to ISIS. But Moallem warned against any unilateral action or strikes in Syrian territory without permission.

Harf said Tuesday, though, that U.S. officials won't be suddenly befriending or working with their counterparts in Syria. Quite the contrary, she said, stressing "we are not going to be coordinating with the Assad regime, period."

"The answer to ISIS is not the Assad regime," the State Department spokeswoman said. "They have allowed them to grow.... And we are not going to be working with them to root out this threat."

In fact, Harf said Obama is asking Congress to fund a "training and equip mission" for the "moderate opposition in Syria." This could be significant, as up until now the U.S. government has resisted giving arms or military equipment directly to anyone in the war-torn country who wants to defeat al-Assad -- in part due to fears such weaponry could end up in the wrong hands, including that of ISIS.

"It is always a challenge that we're dealing with," Harf said. "We believe here, though, that we need to keep supporting the moderate opposition in Syria."

Officials: Non-military ways to defeat ISIS

The key to defeating ISIS isn't necessarily as simple as military might, U.S. officials say.

Yes, airstrikes could block the Islamist terror group's offensive, though they wouldn't necessarily eliminate them entirely if fighters move underground.

"It doesn't take too many people around you getting blown up to make you not want to get out into the open," said retired Col. Peter Mansoor, an ex-aide to former CIA Director Gen. David Petraeus.

From a funding and manpower standpoint, Harf said it's important to cut off funding for ISIS and its supply of foreign fighters like Douglas McCain, the American killed in fighting in Syria over the weekend.

There is also a gut decision of what to do when faced with a terror threat: After beheading Foley, for instance, ISIS promised to kill more Americans so long as they were targeted.