Special operations troops say they should be doing more in the war against the Islamic State group, complaining of strict rules of engagement and White House limits on troop numbers in Iraq and Syria.

Two years after the U.S. went to war, American commandos in relatively small numbers are in at least five countries under Islamic State assault: Syria, Iraq, Libya, Afghanistan and Yemen.

But their role is mostly to train, advise and assist — a limitation that keeps them at arm’s length when local allies go into battle. Overall, the number of deployed American special operations personnel is about a third less today than it was during the troop surges for the Iraq and Afghanistan wars.

The Washington Times interviewed a senior special operations officer who spoke about the frustration of not being able to conduct a series of direct raids on Islamic State leaders.

“We have to say, ‘Mother may I?’ to the White House for any expansion of authorities,” said this war veteran, who asked not to be identified.

This officer indicated that targets are passed up if it is determined that the Islamic State commander is operating and moving with civilians in tow.

“If the bad guy is with women and children, then you cannot strike,” the officer said.

The source said the international laws of armed conflict allow such raids in certain circumstances.

“If you have [the Islamic State’s] No. 3 in the crosshairs and he’s using human shields, would we be able to strike him or not?” the officer asked. “This is an important debate. But are we fighting a war or are we not? They are clearly waging a war against us. Are we waging a war, or are we conducting a police action?

“How do you ‘advise and assist’ someone when you are not allowed to go into combat with them?” the officer added.

Rep. Ryan K. Zinke, a Montana Republican and former member of SEAL Team 6, said he regularly talks with former special operation colleagues. Their chief complaints: Commanders have little latitude in approving targets and the number of U.S. commandos deployed in Iraq and Syria is too small.

“You need to make sure the rules of engagement are conducive to winning,” said the retired Navy commander. “Right now, collateral damage is more important than either the target or, at some times, it is more important than the lives of our troops who are in combat. If we put our troops in harm’s way, you have to set the conditions where, No. 1, we can protect them, and No. 2, they can win.”

Kenneth McGraw, a spokesman for U.S. Special Operations Command, told The Times that SoCom supplies the troops but does not make the rules.

“The geographic combatant command establishes rules of engagement for their area of responsibility,” Mr. McGraw said. “We provide special operations forces to the GCCs. Once [special operations forces] are in a geographic combatant command’s area of responsibility, they are under the command and control of that GCC.”

The constrained commitment is in sharp contrast to how special operations forces hunted al Qaeda terrorists at the height of wars in Iraq and Afghanistan. Yet the Islamic State, with 25,000 fighters, maintains a more numerous and effective force than al Qaeda ever has.

Iraq as the model

Iraq in particular serves as a textbook example of how operators, intelligence collectors, analysts and aviators working cohesively can deal a blow to terrorists in the 2000s.

Troops launched raids daily to bring down what was then called al Qaeda in Iraq. With its leaders killed and captured, the group was all but vanquished in Iraq by 2010.

Numbers provided by U.S. Special Operations Command to The Times show that at the height of military combat, SoCom had about 12,500 people deployed in any week. Today, the average is about 8,000.

Al Qaeda in Iraq leader Abu Bakr al-Baghdadi eventually moved to the power vacuum that was the 2011 Syrian civil war. He organized a terrorist army to seize territory in Syria and Iraq to form a “caliphate” called the Islamic State. The fighters invaded Iraq in the winter of 2013 when no U.S. troops were present to stop him.

President Obama authorized a new war in Iraq in the summer of 2014 that is heavy on training, advising and conducting airstrikes — a far different approach from the large 2005-2011 counterterrorism American task force.

Defense Secretary Ashton Carter in December announced the formation of a limited terrorist-hunting cell, a “specialized expeditionary targeting force” of about 200 U.S. commandos and support staff based in northern Iraq.

“These special operators will over time be able to conduct raids, free hostages, gather intelligence and capture [Islamic State] leaders,” Mr. Carter told the House Armed Services Committee. “This force will also be in a position to conduct unilateral operations into Syria. That creates a virtuous cycle of better intelligence, which generates more targets, more raids and more momentum. The raids in Iraq will be done at the invitation of the Iraqi government and focused on defending its borders and building the [Iraqi military’s] own capability.”

Since his testimony, news has been scant on what the task force has accomplished. The Pentagon has put strict limits on releasing any information at the request of Army Gen. Joseph L. Votel, chief of U.S. Central Command, which runs the war.

But the force does not appear to be operating anywhere near the pace of President George W. Bush’s troop surge in Iraq in the 2000s.

“I’m deeply concerned that this targeting group isn’t heavy enough to move the needle,” Mr. Zinke said.

“I talk to special operations folks a lot, and they are enormously frustrated because they see we can make a difference, and yet the rules of engagement and the process really do not allow them to do what they do best: think out of the box on the front lines.”

Besides this expeditionary strike force, the White House approved about 300 commandos for Syria. They are tasked with advising Syrian Arab and Kurdish coalitions fighting the Islamic State. Earlier this month, Arab forces liberated the town of Manbij in northern Syria, near the Turkish border.

An unspecified number of U.S. commandos are also training and advising Iraqi Security Forces, including its counterterrorism unit.

The targeting force (200), the Syrian advisers (300) and the trainers of Iraqi Security Forces — those are the three arms of the U.S. special operations forces combating the 25,000 fighters in the field for the Islamic State in Syria and Iraq.

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