The Culture Ministry appealed today for "understanding" while the Amphipolis excavation proceeds.
The partially uncovered tomb from the end of Greek warrior-king Alexander the Great's reign, which was found inside the mound, has sparked intense media interest amid wild speculation that it may contain rich treasures or the bones of an ancient celebrity.
Alexander inherited the throne of Macedonia, in northern Greece, from where he set off to conquer a vast empire reaching India.
Alexander died in 323 BC at age 33 and was buried in Egypt
Also Read
Although the precise location of his grave is one of the enduring mysteries of archaeology.
Greek Prime Minister Antonis Samaras has already visited the Amphipolis excavation and state TV daily leads news bulletins with incremental developments about the dig.
So far, archaeologists have uncovered part of the late 4th-century BC tomb's entrance, which has two large marble sphinxes placed on a lintel just under the barrel-vaulted roof.
But the tomb may well have been looted hundreds and hundreds of years ago.
Part of a stone wall that blocked off the subterranean entrance is missing, while the sphinxes originally two meters (6 feet) high lack heads and wings.
Near the sphinxes, excavators have found fragments of a large marble lion that originally capped the mound, which indicates the site was severely damaged and dug up in later antiquity.
Nobody knows yet who the mound was built for.
Alexander's mother, widow, son, brother and sister-in-law were all murdered in separate attacks in the Amphipolis area during the brutal power struggles that followed his death.
Older research has tentatively linked the lion statue, which was removed during Roman times and discovered a century ago some 5 kilometers (3 miles) away, with Laomedon, one of Alexander's military commanders; his admiral, Nearchos, was a citizen of Amphipolis.
"It's all speculation until we see the inside (of the tomb)" said Michalis Tiverios, a professor of archaeology at the University of Thessaloniki.
The excavation is expected to last at least another few weeks.