The possibility that the extremists could damage or destroy the majestic ruins -- considered among the world's most magnificent architectural sites -- has drawn international alarm and calls that the site be protected.
The entire city of Palmyra, also known as Tadmur, has been captured by the militants, said Maamoun Abdulkarim, Syria's general director of antiquities and museums. Syrian news media reported that pro-government forces had retreated in the face of a militant offensive against the town, situated about 130 miles northeast of Damascus, the capital.
The museum, which houses statues and other items from the ancient city, is in Palmyra, which is adjacent to the sprawling archaeological site, once a major tourist destination.
"We know they [the militants] entered into the main hall of the museum, but then they left," Abdulkarim said in a telephone interview. "Also, they've gone into the neighborhoods, into the houses, and have already killed some people they thought to be working with the government. We're waiting to see what's going to happen."
Pro-government accounts on social media said that all inmates in nearby Tadmur prison -- a notorious jail that reportedly holds many government opponents -- had been transferred to an undisclosed location before the city was overrun by Islamic State. The accounts also reported the execution of 17 people by the militant group as punishment for working with the government.
The fate of the 2,000-year-old ruins, a UNESCO World Heritage site, appears to hang in the balance. Abdulkarim has called on the U.S.-backed international coalition fighting Islamic State to help save the monument, which featured Roman-era colonnaded streets, arches and an amphitheater. The site was a key trade terminus in ancient times.
It was unclear whether the Syrian military, which is over-stretched and fighting rebels on numerous fronts, were preparing a counterattack to take back Palmyra. The Obama administration has been waging an air war against Islamic State in Syria and Iraq but is also aiding other groups seeking to overthrow the government of Syrian President
As a precaution, authorities in Palmyra had removed hundreds of statutes from the archaeological complex for safekeeping. But the militants' arrival has spurred fear that the fighters will turns their weapons on the ruins, denouncing them as idolatrous. Islamic State has disseminated images of its followers taking sledgehammers and power drills to ruins and precious museum pieces in Iraq.
Islamic State fighters captured the city late Wednesday or early Thursday after a weeklong battle, forcing the withdrawal of Syrian troops. It appeared to be the first time that the group had taken control of a major city after battling with Syrian forces.
The withdrawal was a significant strategic setback for Syrian forces. Palmyra is situated near major natural gas fields and along a main highway to the eastern province of Dair Alzour and the Iraqi border.
Islamic State controls a broad stretch of territory in Syria and neighboring Iraq. This week, the militants drove Iraqi government forces from the western Iraqi city of Ramadi, capital of Anbar province.
On Thursday, Islamic State distributed photos purporting to show the aftermath of the battle for Palmyra, reported the SITE Intelligence Group, which monitors militant Web traffic. Among other things, the images depict what the militants called a captured hospital, military air base and prison, along with deserted street scenes, destroyed helicopters and bodies said to be those of Syrian soldiers, the SITE group said.
The head of the United Nations' cultural agency has called for an end to hostilities in the area.
"The fighting is putting at risk one of the most significant sites in the Middle East and its civilian population," UNESCO chief Irina Bokova said in a statement.