Barclays agreed to pay $450 million to regulators last week for what authorities said was a "pervasive" attempt for four years to manipulate the London inter-bank offered rate, or Libor.
When banks borrow from each other, they charge each other an interest rate. The Libor is the average of those rates and it is used to establish lending rates on a variety of loans.
"Last week's events have dealt a devastating blow to Barclays' reputation. As chairman, I am the ultimate guardian of the bank's reputation. Accordingly, the buck stops with me and I must acknowledge responsibility by standing aside," Agius said in a statement.
Since the settlement was announced, pressure has been mounting for Barclays to take full responsibility for the bank's actions, The New York Times reported Monday.
Last week, the bank said four top executives, including Chief Executive Officer Robert Diamond, have "volunteered" to forfeit their 2011 bonus compensation.
But several prominent politicians have called for Diamond to step down, as well, the Times said.
The bank said Agius would stay at his job until a replacement could be found. Diamond, meanwhile, is scheduled to testify in Parliament Wednesday.
Diamond has not offered to resign, but said in a letter last week this kind of conduct "has no place in the culture of Barclays."