WASHINGTON — U.S. radar showed Syrian warplanes in the vicinity of the suspected chemical-weapon attack that killed dozens of people in northern Syria on Tuesday, according to a senior Defense Department official.

The gas attack killed several children, prompting President Trump on Wednesday to say that it “had crossed a lot of lines for me.” Trump did not promise a military response to the use of chemical weapons on civilians, a widely condemned atrocity.

But the Defense official, who was not authorized to speak publicly about intelligence matters, said that a military response could imperil U.S. forces on the ground in Syria fighting the Islamic State.

There are several hundred U.S. special operations troops in Syria advising forces arrayed against the Islamic State, also referred to as ISIS or ISIL. A U.S. attack on the Syrian regime of Bashar al-Assad could prompt him to target American troops, deepening and complicating the civil war there, the official said.

That opinion is echoed by Chris Kozak, an analyst at the Institute for the Study of War.

A key risk, Kozak said, is that any option that weakens the regime would also probably boost the power of the Islamic State, which has been fighting the Assad regime.

No option would be a game changer, Kozak said, including broadening existing sanctions and attempting to aim them also at Russians and Iranians helping the regime.

But a limited strike with weapons such as cruise missiles fired at regime airfields, or at assets owned by Assad's family, could send the message that such attacks will no longer be tolerated, said Nicholas Heras, an expert on Syria at the Center for a New American Security.

Heras pointed out that the Israelis have conducted airstrikes in Syria in the last two years and have not been attacked by Assad, blunting the argument that U.S. troops would be put at risk.

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Excessive caution carries risks, too, said Michael O'Hanlon, a military analyst at the Brookings Institution. The failure by the West to act in Rwanda and the Balkans during conflicts there made matters worse.

"We have to avoid deterring ourselves out of excessive fear," O'Hanlon said.

A limited U.S. military response is possible, he said, but more important is finding a way to end the civil war there that has claimed 500,000 lives.