The British Museum was warned precious artefacts were allegedly being stolen and sold online two years ago but bosses insisted “all objects were accounted for”, it is reported.
Art dealer Ittai Gradel contacted the museum in February 2021 after spotting items he had seen in its catalogues.
Mr Williams added there had been a “thorough investigation” and that the “collection was protected”.
Last week the British Museum announced that items from its collection were found to be “missing, stolen or damaged” and an unnamed member of staff has been sacked.
Reports have said the number of stolen artefacts from the British Museum is “closer to 2,000” with the total value of missing pieces thought to run into “millions of pounds”.
An independent review of security has been launched and the matter is also under investigation by the economic crime command of the Metropolitan Police.
An eBay spokesman said: “Our dedicated law enforcement liaison team is in close contact with the Metropolitan Police and is supporting the investigation into this case.
“We do not tolerate the sale of stolen property. If we identify that a listing on our site is stolen, we immediately remove it and work with law enforcement to support investigations and keep our site safe.”
Dr Gradel’s emails suggest he became suspicious when he “stumbled” upon a photo of a Roman cameo fragment that he said had been up for sale and had been listed on the British Museum website but had since been removed.
He alleges in one of his emails that a third-party seller returned a gem to the museum as soon as Dr Gradel told him his suspicions, but claims the museum didn’t follow this up sufficiently.
In one of several emails he sent to follow up any progress, this time to a board trustee, Dr Gradel accuses the director - Hartwig Fischer - and Mr Williams of “sweeping it all under the carpet”.
Labour MP Ben Bradshaw, a former culture secretary, said the latest allegations were “extremely serious”.
“These are priceless objects that belong to the nation, and they should be safe,” he told BBC News.
“This has potential reputational damage for Britain because this is already being reported across the globe. The British Museum is a probably the world’s most famous museum.”
A museum source told the Telegraph that the directorate’s handling of the case has been “negligent and incompetent” and that evidence presented to them was ignored.
An antiquities expert reportedly told the museum three years ago that items from its collection were being offered for sale on eBay, with one Roman object, valued at £25,000 to £50,000 by dealers, offered for just £40.
The independent review will be led by former museum trustee Sir Nigel Boardman, and Lucy D’Orsi, chief constable of the British Transport Police, who will “kickstart” a “vigorous” programme to recover the stolen items.
The British Museum declined to comment while the police investigation is on-going.