BEIRUT — The United States and its allies are trying to organize a coalition to push back the Islamic State group in Iraq. But any attempt to destroy the militants or even seriously degrade their capabilities means targeting their infrastructure in Syria.

That, however, is far more complicated. If it launches airstrikes against the group in Syria, the United States runs the risk of unintentionally strengthening the hand of President Bashar Assad, whose removal the West has actively sought for the past three years. Uprooting the Islamic State group, which has seized roughly a third of Syria and Iraq, may potentially open the way for the Syrian army to fill the vacuum.

The alternative would be to finally get serious about arming the mainstream Western-backed rebels fighting to topple Assad. But there is a reason the Obama administration has been deeply reluctant to throw its weight behind them.

The relatively moderate rebel factions fighting in Syria are in tatters. There are no secular groups, and the strongest factions are Islamic groups, many of which work with al-Qaida’s official branch in Syria, the Nusra Front.

The Nusra Front, which has somewhat dropped from international headlines because of the Islamic State group’s exceeding brutality, is on the U.S. list of terrorist groups and is still active.

It and other rebels recently seized the Quneitra border crossing between Syria and the Israeli-held Golan Heights, taking 45 United Nations peacekeepers hostage. It was also among a group of militants that recently overran a Lebanese border town and is holding several Lebanese soldiers and policemen captive.

While the United States and its allies are now arming Kurdish peshmerga fighters in Iraq against the Islamic State group, Syrian rebels complain they are largely on their own, battling both the militants and the tyranny of Assad.

The Syrian opposition and many Syria observers are convinced that the rapid rise of the Islamic State group is a result of the United States having let the Syrian conflict fester for so long.

President Obama kicked up a storm of criticism late last month when he said “we don’t have a strategy yet” for dealing with the Islamic State group in Syria.

“It is very important from my perspective that when we send our pilots in to do a job, that we know that this is a mission that’s going to work, that we’re very clear on what our objectives are, what our targets are,” Obama said.

His statement epitomizes the caution that many say has been at the heart of U.S. foreign policy on Syria for the past three years. For better or for worse, Obama has avoided wading into the Syria mud, resisting pressure to directly arm the rebels in part because of fears the weapons would only end up in extremists’ hands.

Last year, the United States threatened to bomb Assad’s forces after a deadly chemical weapons attack blamed on his government. It backed away at the last minute. Though he had to give up his chemical weapons stockpile, an emboldened Assad made significant advances against outgunned rebels in key areas, particularly around Damascus.

Members of the Obama administration have said they recognize the need to address the Syria side of the equation. While meeting with NATO foreign and defense ministers on possible action in Iraq, Secretary of State John Kerry said there are obviously “implications about Syria in this.”

A senior Obama administration official said Thursday that the United States wanted to establish a credible ground force in Syria by training more moderate rebels before taking military action there.

The United States signaled back in June that it hopes to enlist moderate Syrian opposition fighters in the battle against militant extremists.

Obama sent Congress a $500 million request for a Pentagon-run program that would significantly expand previous covert efforts to support the rebels. The request is still pending.

Still, such a program faces the same questions hanging over U.S. policy the past three years – how to distinguish “moderate” rebels from others in an increasingly radical landscape and how to ensure weapons reach only those groups.

Airstrikes alone would likely do little to truly defeat the Islamic State if there is no force on the ground to seize territory as the radicals retreat. Western leaders have categorically rejected the notion of partnering up with Assad, whom they accuse of committing war crimes on his own people.