The vicious Islamic State group now is vowing to broaden its war campaign to include killing Americans wherever and whenever it can.

Tuesday’s horrific videotaped beheading of American photojournalist James Foley was packaged with a new Islamic State posting on social media threatening the United States: “We will drown all of you in blood.”

A visibly angered President Obama gave a stern reply Wednesday afternoon, saying in a televised address that the U.S. and its allies will work together to “extract this cancer” that is the Islamic State.

“ISIL speaks for no religion. Their victims are overwhelmingly Muslim, and no faith teaches people to massacre innocents,” Mr. Obama said. “No just God would stand for what they did yesterday, and for what they do every single day. ISIL has no ideology of any value to human beings.”

Just hours after Mr. Obama spoke, the White House revealed that the president had authorized a secret military mission this summer to a site in Syria in a bid to free Mr. Foley and other Americans held by the terrorist group, but the hostages were not there.

“The U.S. government had what we believed was sufficient intelligence, and when the opportunity presented itself, the president authorized the Department of Defense to move aggressively to recover our citizens,” said Lisa Monaco, assistant to the president for homeland security and counterterrorism. “Unfortunately, that mission was not successful because the hostages were not present.”

The White House did not reveal exactly when or where in Syria the mission took place. Citing administration sources, The Associated Press reported that a “number of militants” were killed in the operation and one American sustained a minor injury.

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The president also offered his condolences via telephone to Mr. Foley’s parents, who also praised their son for his life’s work.

Speaking to reporters in front of their New Hampshire home, John and Diane Foley noted his dedication in documenting Syria’s conflict and the plight of ordinary Syrians. “We believe he was a martyr for freedom,” John Foley said.

In the video, the terrorist group said it was beheading James Foley in retaliation for U.S. airstrikes against its positions in northern Iraq.

The White House said earlier this month that the Islamic State is not a threat to Americans — a position deemed “utter hogwash” by Robert Spencer, director of Jihad Watch, which monitors Islamic extremism.

“The White House says that the U.S. is not at war with the Islamic State,” Mr. Spencer said. “But the Islamic State certainly is at war with the U.S.”

A U.S. intelligence official said Thursday, “I would tell you ISIL has had a longstanding, overt interest in killing Americans.”

Mr. Spencer said there is ample evidence that the terrorist group — which controls large portions of Iraq and Syria and has committed mass executions — is gearing up for attacks against the U.S.

The U.S. government believes some Americans have joined the Islamic State and, programmed to conduct suicide bombings, will pose risks upon their return.

Britain says hundreds of its nationals have joined the militants and have committed some of its most brutal killings. British authorities said Wednesday that they suspect the black-clad executioner in Tuesday’s beheading video is a Briton.

Prime Minister David Cameron said the man had not been identified, but “from what we have seen it looks increasingly likely that is a British citizen.”

Germany and France say about 1,300 of their nationals have joined jihadist groups, including the Islamic State, The Associated Press reported.

In the U.S., the Islamic State flag has appeared sporadically as the terrorist group’s propaganda arm tries to recruit young killers.

“They have said they are going to go after Americans,” Mr. Spencer said. “They have said American civilians are all legitimate targets. It seems to be absolutely certain they will be trying to kill as many Americans as possible in the United States as well as elsewhere.”

Retired Army Gen. John M. Keane, who is pressing the White House to adopt a broad campaign against the Islamic State, agrees that the terrorist organization of more than 10,000 fighters represents wider threat.

“[The Islamic State] is the new face of al Qaeda and is a threat to U.S. vital interests in the Middle East and a threat to the safety and security of the American people,” Mr. Keane said. “Despite some limited setbacks in northern Iraq, IS maintains the initiative and freedom of movement throughout Iraq and Syria. What the U.S. needs is not just rhetoric condemning this barbarism but a U.S.-led strategy with our allies to first stop IS and then defeat them.”

The Islamic State has perfected the car bomb as a weapon. After U.S. troops left Iraq in 2011, it unleashed waves of suicide and remotely detonated car bombs throughout Baghdad and other cities.

A Canadian member of the Islamic State was quoted as saying he is training others on how to build such deadly weapons — a hint that such vehicle-borne improvised explosive devices may show up in his home country.

Retired Army Lt. Gen. William Boykin, formerly the Pentagon’s No. 2 intelligence official, said the Islamic State’s game plan is to threaten the U.S. repeatedly to raise its stature among young potential jihadists.

He said the terrorist group also believes it can intimidate Mr. Obama into halting the roughly 75 airstrikes that have helped Iraqi Kurds protect their capital of Irbil and retake the Mosul Dam.

“The notion is that Barack Obama is weak right now and he will fall back on appeasing his base, which is very much against any continuation of military ops in Iraq,” Gen. Boykin said. “I personally believe that this notion is a miscalculation by IS. Obama is under too much pressure now from inside his own party to try to convince anyone that the U.S. should declare victory and go home.”

The Obama administration has sent mixed messages on the threat posed by the Islamic State, which previously called itself the Islamic State in Iraq and the Levant.

In January, Mr. Obama seemed to brush off any dangers, comparing it in an interview with The New Yorker to a “JV team” compared with al Qaeda.

After the Islamic State army in June swept out of Syria into northern Iraq and took the large city of Mosul and then moved south toward Baghdad, Defense Secretary Chuck Hagel had a new perspective.

“Make no mistake, and this country should not make any mistake on this, nor anyone in Congress — ISIL may not appear to be an imminent threat to the United States,” he said. “It is a threat to the United States. It is a threat, a clear threat to our partners in that area, and it is imminent.”

But two weeks ago, Deputy National Security Adviser Tony Blinken said no, the Islamic State is not a threat to Americans.

“Right now, their focus is not on attacking the U.S. homeland or attacking our interests here in the United States or abroad,” Mr. Blinken told CNN’s Jake Tapper.

White House officials attempted to portray this summer’s failed rescue mission as proof that the U.S. will do whatever it can to rescue Americans held captive abroad.

“The president could not be prouder of the U.S. forces who carried out this mission,” Ms. Monaco said. “Their effort should serve as another signal to those who would do us harm that the United States will not tolerate the abduction of our people and will spare no effort to secure the safety of our citizens and to hold their captors accountable.”

On Wednesday, a senior Pentagon official said the State Department is seeking a small boost in troop numbers in Iraq, similar to the incremental increases the Obama administration has approved for the U.S. military operation in the northern part of the country.

“There is a request by the State Department for additional U.S. personnel, and my understanding is that it’s for less than 300 [troops],” the official said.

The Obama administration has placed 849 military personnel in Iraq and tasked them with conducting airstrikes, conducting assessments and providing Iraqi forces with intelligence, Pentagon officials said.

Additionally, the framework for an international coalition to combat the Islamic State began to form Wednesday, when Germany and France said they were willing to help Kurdish fighters battle the militants.

Germany and Italy announced Wednesday that they were prepared to join Britain and France in delivering weapons and other military gear such as helmets and security vests to the Kurdish fighters.

• Ben Wolfgang and Maggie Ybarra contributed to this article, which is based in part on wire service reports.

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