The agency is currently embroiled in a lawsuit filed by Andersen, who is claiming wrongful termination, retaliation and discrimination.
Rapp has now filed a response to that suit, describing his sacking as "lawful and appropriate".
The agency alleged he had failed in "basic duties" towards the agency, claiming he had "failed to engage" with Rapp's clients and its senior executives.
The response does not go into further detail, but does say: "Indeed, by contributing so little as Rapp US's president, Mr Andersen has demonstrated that both he and position were unnecessary - Rapp has not hired a successor and has no plans to do so."
The agency adds that Andersen was given "repeated warnings" before his dismissal.
Rapp's response does not address Andersen's specific allegations against Alexei Orlov, but describes them generally as "outrageous" and as "gross mischaracterisations".
The thrust of Rapp's legal defence is to play down the validity of Andersen's claims. It is moving for a dismissal of those claims and for recovery of costs.
Andersen filed his lawsuit in May with a list of extensive allegations against the Omnicom agency and particularly Orlov. It described him as a "destructive force" and listed several alleged incidents involving colleagues. Andersen claims Orlov described women as "fat cows" and stereotyped a Jewish colleague as "miserly". He claims he was fired as a consequence of complaining about Orlov's behaviour.
Andersen is not the only ex-Rapp staffer to have concerns. Multiple sources, including former vice-president for business development Alison Clark, pointed Campaign to the exodus of staff from Rapp London, claiming a wider culture of bullying.