In a statement, Mr Agius said: "The buck stops with me."
Last week Barclays was fined £290m ($450m) for attempting to manipulate the Libor inter-bank lending rate.
Barclays' chief executive Bob Diamond will appear before MPs on the Treasury Committee on Wednesday.
Mr Agius is due to answer their questions on Thursday.
Mr Agius has also stepped down as chairman of the British Bankers' Association, which is responsible for compiling Libor.
But, Barclays said Mr Agius would remain in his post at the bank until "an orderly succession is assured".
Mr Agius, who also serves on the BBC's executive board, said last week's events were evidence of "unacceptable standards of behaviour within the bank".
He said the findings had "dealt a devastating blow" to Barclays' reputation. More
The statement in the headline applies to not only the financial industry, but also to the nuclear industry (with hindsight into Fukushima), governments which are being unduly influenced by corporate lobbyists and the oil companies. Corporate Social Responsability must become the norm. Editor
