About 2,000 items are thought to have been stolen from the British Museum, but some of the missing treasures have started to be recovered, chairman George Osborne has confirmed.
The ex-chancellor accepted the museum's reputation has suffered but said "it is a mess we are going to clear up".
A staff member the museum suspects of involvement has been sacked.
And it was announced on Friday that Hartwig Fischer, the museum's director, will step down after accepting a 2021 investigation was mishandled.
The museum, one of the UK's most prestigious cultural institutions, has been under pressure since revealing earlier this month that a number of treasures were reported "missing, stolen or damaged".
The items involved dated from the 15th Century BC to the 19th Century AD and had been kept primarily for academic and research purposes, the museum previously said.
Mr Osborne - who was appointed as chair of the museum in June 2021 - told BBC Radio 4's Today programme that "we have already started to recover some of the stolen items".
Asked where the missing items were located, he said "some members of the antiquarian community are actively cooperating with us" and that recoveries so far were a "silver lining to a dark cloud".
He said he was confident that "honest people" will return items found to have been stolen, but acknowledged that "others may not".
Founded in 1753, the British Museum has amassed a collection of around eight million items, but as of 2019 only around 80,000 were on public display, with the rest held in storage.
Mr Osborne said that not all of the items are "properly catalogued and registered" and suggested "someone with knowledge of what is not registered has a big advantage in removing" them.
The museum is working closely with the police, Mr Osborne said, adding that a "forensic job" is under way to establish precisely what is missing. He said security at the museum needed to be improved.
"It has certainly been damaging to the British Museum's reputation, that is a statement of the obvious, and that is why I'm apologising on its behalf," Mr Osborne added.
A man has been interviewed by Metropolitan Police detectives over the missing items but no arrests have been made.
Senior figures at the museum have scrambled to address how they handled the discovery of missing items after it emerged concerns about potential thefts were first raised two years ago.
Asked why concerns raised in 2021 were not taken seriously, Mr Osborne said he did not believe there was a "cover-up" at the top of the museum, but said it was "possible" that "groupthink" among senior staff meant they "could not believe that there was an insider" stealing treasures.
Mr Fischer, who has held the position of director since 2016, confirmed on Friday that he would leave his role once an interim replacement had been appointed.
He was previously due to step down in 2024.
In a statement, he said: "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.
"The responsibility for that failure must ultimately rest with the director."
He also apologised for "misjudged" remarks alleging the antiques dealer who first raised concerns in 2021 had withheld information about the missing items.
Deputy director Jonathan Williams - who was involved with the 2021 investigation - will step back from his normal duties temporarily until an independent review launched by the museum concludes.
The missing-treasures scandal has prompted questions about the British Museum's wider role as an institution housing objects from around the world.
Greek archaeologist Despoina Koutsoumba told the BBC this week the Parthenon sculptures are "not safe" in London. The Greek government has long called for the artefacts, often called the Elgin Marbles, to be returned to Greece.
Tim Loughton MP, the Conservative chairman of the all party parliamentary group for the museums, has rejected claims it is no longer a trusted custodian of its vast collection.
He said calls for artefacts to be returned to their countries of origin were "opportunistic", telling BBC News culture and media editor Katie Razzall other countries should be "rallying around to help retrieve objects instead of trying to take advantage".
Mr Osborne said the British Museum plays a vital role in bringing together important collections from around the world, adding: "In an age that we are always reminded what divides us, it is a place that reminds us of what we have in common."