Molly’s family found she had been viewing graphic images of self-harm on the site prior to her death.
Adam Mosseri said Instagram was trying to balance “the need to act now and the need to act responsibly”.
He added the site was “not where we need to be on the issues of self-harm and suicide”.
When asked by the BBC’s Angus Crawford when the images would be removed, Mr Mosseri replied: “As quickly as we can, responsibly.”
Digital minister Margot James told BBC Radio 4’s PM programme the government would “have to keep the situation very closely under review to make sure that these commitments are made real – and as swiftly as possible”.