Abdulkarim also confirmed the jihadist group had raised its flag over the ancient citadel that overlooks some of the spectacular Greco-Roman ruins in the city.
Speaking at a news conference in Damascus, he said some modern plaster statues in the museum had been destroyed but he did not report any damage to antiquities in the building.
The jihadists on Thursday "entered the museum and broke some plaster statues... that were being used to represent life in prehistoric eras."
They returned on Friday, and when they left, "they closed the doors behind them and placed their guards" at the entrance of the museum, Abdulkarim said, citing residents still in the town.
Most of the antiquities in the museum were removed and brought to Damascus before Daesh cemented its control of Palmyra on Thursday.
"There's almost nothing left in the museum. We had been progressively transferring the antiquities to Damascus," he told AFP after the news conference.
"But there are still the large items, like the sarcophagi, which weigh three or four tonnes and we could not move. Those are what worry me."
The Roman-Byzantine sarcophagi feature high-relief carvings.
Abdulkarim also confirmed Daesh fighters had raised their black flag over the 13th century Mamluk Fakhr al-Din al-Maani citadel that overlooks the ruins of Palmyra.
Earlier, a photograph purporting to show Daesh flag over the citadel was circulated on social media, but it was not possible to confirm its authenticity.
Both the citadel and the ruins are on the UNESCO World Heritage list, and before the war some 150,000 tourists a year visited Palmyra.
"There has been no movement (of Daesh) in the archaeological site," Abdulkarim said, referring to the main ruins in the city, including its famed colonnaded streets and extensive necropolis.
The arrival of Daesh in Palmyra has caused international concern about the fate of the city's historical treasures, because the group has destroyed heritage sites in areas under its control in neighbouring Iraq.
"I hope that they do not repeat the same destruction they committed in Iraq," Abdulkarim said.
"We will consider measures to prevent them from destroying Syrian cultural heritage."
A Syrian activist who identifies himself as Mohammed Hassan al-Homsi said "traffic was back to normal" on Saturday in Palmyra and that regime warplanes did not bombard the city.
Speaking to AFP, he said the jihadists had allowed motorists to drive to Daesh stronghold of Raqa, further north, to stock up on vegetables.
Homsi said Daesh fighters had used loudspeakers at mosques to tell government employees to return to work as well as order women to wear the niqab -- a veil that covers the face.
Syria's official SANA news agency reported, meanwhile, that regime warplanes carried out a series of raid on Daesh targets east of the central province of Homs "killing terrorists" and destroying equipment.