The bank chief also said he "welcomes" the opportunity to give evidence to Parliament in the coming weeks.
Last night, he accepted a summons from the Commons Treasury Select Committee to appear before the influential cross-party panel to answer for the bank's behaviour.
In a letter to the committee's chairman, Tory MP Andrew Tyrie, he accepted that foregoing bonuses, apologising, paying the fines and disciplining individual offenders would not be sufficient to restore the bank's reputation.
He said he would "welcome the opportunity to provide answers" when he gives evidence in the coming weeks.
Mr Diamond said "a small number" of individual traders were responsible for one part of the scandal - entirely to benefit their own pockets - and that insufficient controls had now been strengthened.
But he also accepted that a corporate decision to cheat the system was "wrong" even if it was aimed at protecting the bank from "negative speculation during periods of acute market stress".
"Given the nature of the behaviours uncovered through these investigations, questions of accountability have rightly been raised," he wrote.
"We are now completing a review of employee conduct for all of those involved.
"That process is rigorous and all appropriate options will be pursued for those who have a case to answer, ranging from the clawback or withholding of remuneration to being asked to leave the bank."
The decision to abandon bonuses was also an important act, he said.
"But we need to do more than that. We need to work every day to rebuild the trust that has been damaged by these actions and others that have come before them.
"This kind of conduct has no place in the culture of Barclays."
Prime Minister David Cameron said it was very important that accountability for what went on "goes all the way to the top of that organisation" and that Mr Diamond had "some serious questions to answer".
In a further blow, the Financial Times called directly on the senior banker, who it said was behind the bank's "hard-driving culture", to step down.
"If he had an ounce of shame he would immediately step down," the newspaper said in a front page editorial.
The sector was also braced for its public image to take a further battering with the Financial Services Authority (FSA) due to reveal it has found evidence that banks are embroiled in another scandal.
A review into the way lenders pushed so-called interest rate swap arrangements (Irsas), which have landed small businesses with spiralling bills, is expected to have uncovered mis-selling.
Barclays shares slid 15% yesterday - wiping £3bn from its market value - as investors ditched the stock amid fears £290m fines could be dwarfed by lawsuits and damages.
At the start of the trading day, Barclays shares bounced back a little, and were up just over 4%, but have sinced turned around and dropped 0.4%.
The bank was hit with the penalties by UK and US regulators for fixing the interbank lending figures that affect millions of homeowners and small firms.
The controversy, which covers a period between 2005 and 2009, could spread to other lenders, as RBS (LSE: RBS.L - news) , HSBC (LSE: HSBA.L - news) , UBS (NYSEArca: DJCI - news) and Citigroup (NYSE: C - news) are also being investigated.
Serious Fraud Office investigators are in talks with the Financial Services Authority (FSA) over the scandal.
Mr Diamond, who was in charge of Barclays Capital at the time the breaches occurred, along with three other key executives, waived their bonuses for this year.
Meanwhile, RBS has played down reports in the Times which claim that it faces a £150m fine for manipulating Libor.