British Museum missing 2,000 artefacts after police called in
The UK's former chancellor described the missing pieces as "small items of jewellery, gems, bits of gold that were not on public display".
He told BBC radio it was still not clear exactly how many items had gone astray.
"I will give you an estimate of around 2,000. But I have to say that’s a very provisional figure," Osborne said.
"We have started to recover some of the stolen items, which is a silver lining to a dark cloud."
Museum director Hartwig Fischer resigned on Friday, admitting the institution did not act "as it should have" on warnings that items had gone missing.
The central London museum said last week it had dismissed a staff member and alerted the police after artefacts were found to be "missing, stolen or damaged".
One of the British capital's biggest tourist draws, the museum is best known for housing collections that include the Rosetta Stone and the Parthenon Marbles.
Osborne attributed management's failure to act on warnings to "groupthink" that "just couldn’t believe that an insider was stealing things, couldn’t believe that one of the members of staff were doing this".
"We believe we’ve been the victim of thefts over a long period of time and, frankly, more could have been done to prevent them," he said, adding that security at the museum had been tightened.
The antiquarian community was cooperating with the museum to help return some of the missing pieces, he said.
The Metropolitan Police confirmed on Thursday that a man had been interviewed in connection with alleged thefts.
The force said no arrests had been made and it would continue to work "closely" with the British Museum as inquiries continue.
Fischer, a German art historian, said he would step down with immediate effect because of lapses in procedures that allowed the items to be taken.
"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," he said.