A spokesman for the Prime Minister said Mr Agius' position as a Government adviser had been "linked to his role at Barclays".
Mr Agius will be expected to give evidence to MPs this week, along with Bob Diamond, the chief executive of the scandal-hit bank.
It also emerged that Paul Tucker, the deputy governor of the Bank of England, will be called in front of the Treasury Committee to explain a key phone call with Mr Diamond about the Libor rate.
After Mr Diamond spoke to Mr Tucker, Barclays staff came to believe the Bank of England wanted them to falsify the data used to calculate Libor by submitting lower rates.
The bank’s traders then escalated their secret attempts to manipulate the markets and make it appear that the bank was paying less to borrow money than was actually the case.
Both banks insist this was the result of a “misunderstanding” and Mr Tucker had not sanctioned Barclays’ actions.
This morning, a spokesman for the Prime Minister said it was "right" that Mr Tucker appears before MPs to answer questions on what he told Barclays.
At the time the Bank of England was keen to see a lower Libor rate, as that would have been a positive sign in the depths of the credit crunch.
However, the Bank of England last night insisted it was “nonsense” to suggest that it was aware of any impropriety in the setting of Libor.
A spokesman added: “If we had been aware of attempts to manipulate Libor we would have treated them very seriously.”
Mr Diamond will also face questions about how his more junior staff came to believe they should manipulate data about Libor.
He remains under pressure to step down, although City experts claimed it would be difficult for a large bank to cope with the resignation of both its chairman and chief executive.
