Some of the 2,000 artefacts that were stolen from the British Museum have been recovered, said George Osborne, the chairman of its trustees.
Speaking on Saturday, Mr Osborne also said “groupthink” may have prevented museum leaders from believing that treasures had been taken.
His comments came after the resignation of British Museum director Hartwig Fischer on Friday following the series of thefts at the institution.
Deputy director Jonathan Williams has also agreed to step down until an independent review into the thefts has concluded, the museum said.
Metropolitan Police officers have interviewed a man in connection with the missing items but no arrests have been made, it said on Thursday.
The former chancellor told BBC Radio 4's Today programme on Saturday that a "forensic" inquiry was being conducted to find out what had been stolen.
"We think it's around 2,000 items," he said. "But I have to say that's a very provisional figure and we're still actively looking."
"We've already started to recover some of the stolen items," he added, without giving any details of what had been recovered or how.
The London institution is working with the art loss register and members of the antiquarian community who are helping to return some of the missing items, he said, adding that security has been stepped up around museum storerooms.
The artefacts stolen were "small items of jewellery, gems, bits of gold that were not on public display".
Mr Osborne said: “Hartwig Fischer, Jonathan Williams, the deputy director, you know, these are honourable people who have also given their lives to work in the museum sector.
“I don't myself believe there was a sort of deliberate cover-up, although the review may find that to be the case.
“But was there some potential groupthink in the museum at the time, at the very top of the museum, that just couldn't believe that an insider was stealing things, couldn't believe that one of the members of staff were doing this? Yes, that's very possible.
“You know, we wouldn't be the only institution that has fallen foul of that.”
On Friday, Mr Fischer said it was evident the museum had failed to react appropriately to allegations of theft and that failure was his responsibility.
“Over the last few days, I have been reviewing in detail the events around the thefts from the British Museum and the investigation into them,” he said in a statement.
“It is evident that the British Museum did not respond as comprehensively as it should have in response to the warnings in 2021, and to the problem that has now fully emerged.
“I have offered my resignation to the chairman of the trustees, and will step down as soon as the board have established an interim leadership arrangement. This will remain in place until a new director is chosen.”
Almost 2,000 items were reportedly taken, including Roman jewellery, glass and gemstones.
Ittai Gradel, an author, academic and antiquities dealer, had alerted the museum to some of the stolen items, but was ignored.
The responsibility for the “failure” to respond to the thefts “must ultimately rest with the director”, Mr Fischer said.
“I also misjudged the remarks I made earlier this week about Dr Gradel. I wish to express my sincere regret and withdraw those remarks.”
Those remarks questioned how open Dr Gradel had been with the museum in 2021, with Mr Fischer saying he had “reason to believe” Dr Gradel had withheld information on other missing items. Dr Gradel said, however, that this was “an outright lie”.
Dr Gradel said Mr Fischer's resignation was “the right thing to do”.
The value of the artefacts missing from the British Museum runs into the “millions”.
The institution, one of the world's most famous museums, has revealed it is taking legal action against an unnamed member of staff – who was sacked – after the items were discovered to be missing, stolen or damaged this year.
The museum has not revealed how many items were stolen, saying only that they were “small pieces”, including “gold jewellery and gems of semi-precious stones and glass dating from the 15th century BC to the 19th century AD”.
An independent inquiry has been launched and the matter is also under investigation by the Metropolitan Police's economic crime unit.
Museum trustees have said they will find an interim leader.
“I am clear about this: we are going to fix what has gone wrong. The museum has a mission that lasts across generations,” Mr Osborne said.
“We will learn, restore confidence and deserve to be admired once again.”
In July, Mr Fischer, who has been in the job since 2016, had announced he would be stepping down next year.
The British Museum opened in 1759 and houses a number of contested artefacts, including the Elgin Marbles, which British diplomat Lord Elgin removed from the Parthenon temple in Athens in the early 19th century, when Greece was under Ottoman rule.
Another controversial item is the Rosetta Stone, which was found in Egypt, and dates to about 200BC. It was discovered by French troops in 1799 but acquired by Britain under a treaty in 1802.