Brother Edmund Garvey initiated judicial review proceedings on Monday, but in a statement this morning he said that the decision not to proceed is now being communicated to the court.
In September, members of the Drogheda Borough Council voted to effectively rescind the Freedom of Drogheda from him.
The civic honour had been given to the Drogheda native in 1997.
Five councillors voted for the motion to no longer acknowledge Brother Garvey as a freeman of Drogheda.
Four councillors voted against and one member was absent.
Br Garvey was head of the religious order in Ireland when it adopted a legal strategy to defend civil cases taken by victims seeking compensation for historical child sexual abuse.
The strategy means the Christian Brothers has not put forward a nominee to represent it as a defendant in civil cases, which means there is no organisation for victims to sue.
Instead, plaintiffs have to sue all individual Christian Brothers who were members of the order at the time of the alleged abuse.
The approach, while legal, can make it difficult for plaintiffs to pursue their cases.
It was for this reason that some victims had called on councillors to rescind the honour from Br Garvey 26 years after he received it.
Brother Garvey retired from his role as the provincial leader of the Christian Brothers last year.