A man walks past the rubble of damaged buildings after an airstrike in the rebel-held area of Aleppo's Baedeen district, Syria. (Reuters/Abdalrhman Ismail)

Throughout the ongoing U.S. election season, the bloody and protracted war in Syria has hung like a dark cloud. It remains unclear how either candidate would handle the war.

One candidate, Democrat Hillary Clinton, was once one of the strongest advocates for U.S. intervention in Syria. Her Republican rival, Donald Trump, has attacked her for a number of her foreign policy moves and generally favors an isolationist approach. Trump has also repeatedly suggested that Syrian refugees and other immigrants pose such a security threat to the United States that they should be turned away.

A new poll from the Chicago Council on Global Affairs suggests that many Americans feel trepidation about U.S. involvement in the Syrian civil war. While they may favor some U.S. military action in the country, they oppose sending combat troops, arming anti-government groups or negotiating a peace agreement with Syrian President Bashar al-Assad.

In total, 72 percent of Americans were found to favor conducting airstrikes against violent Islamist extremist groups, and 57 percent supported sending Special Operations forces into Syria to fight these groups — two military actions that have already begun under the Obama administration.

However, there was less support for new measures. A slim majority, 52 percent, said they favored a no-fly zone that would include the bombing of the Syrian regime's air defenses, but only 42 percent favored sending ground troops in to fight violent Islamist extremist groups in the region. In addition, just 26 percent favored sending arms to anti-government groups, but a similarly low 31 percent wanted the United States to help negotiate an end to fighting that would keep Assad in power.

In general, supporters of both major political parties were fairly in line with each other, with Republicans slightly more in favor of military action than Democrats — more than half of Republicans (53 percent) favored sending ground troops in to fight extremists, for example, whereas just 42 percent of Democrats and 32 percent of independents agreed.

There's one key aspect of the Syrian war — in fact, perhaps the most high-profile humanitarian angle to the conflict — where the different political schools of thought clearly disagree: refugees. Among Democrats, 56 percent favor taking in Syrian refugees, but only 18 percent of Republicans (and 32 percent of independents) do.

The poll was conducted June 10-27 for the Chicago Council by GfK Custom Research among a national sample of 2,061 adults. The margin of error ranges from ±2.2 to ±3.5 percentage points, with higher margins of error for partisan subgroups.

More on WorldViews

Trump supporters see the world very differently than other Republicans

How Clinton supporters view the world differently than Sanders supporters