The advertising firm, still trying to regroup following its bitter separation earlier this month from one of its founders, Maurice Saatchi, has accused Mr Muirhead of breach of contract after his decision also to leave the agency.
The US lawsuit is being brought against Mr Muirhead in parallel with legal actions already being pursued in Britain. The US action includes a claim that Mr Muirhead - who later agreed to join Mr Saatchi in creating a rival agency - stole Saatchi files from his Manhattan office.
Mr Muirhead's lawyers asked the judge to dismiss the suit on the grounds of insufficient evidence and unnecessary duplication with actions in the UK.
Judge Herman Cahn deferred a decision on the request for several days. Mr Muirhead's lawyers expressed confidence that the case would either be dismissed or severely limited in its scope. "He made it clear that he is not going to let the other side convert this into a free-ranging litigation," said Les Fagen, one of the legal team.
Mr Muirhead, who was in Britain yesterday, is said to be enraged over the US lawsuit and in particular over the suggestion that he is a thief.
Mr Fagen said: "What is so offensive is that they [Saatchi] chose to obtain a tactical advantage really by defaming Mr Muirhead with these outrageous accusations."
Mr Fagen said he believed the Saatchi case to be based on the word of a lift-service representative who apparently saw Mr Muirhead leaving his former Manhattan office on a Saturday afternoon early this month with a box of files under his arm.
Sources close to Mr Muirhead have said the box contained only personal files and a bank statement.
The defence also highlighted yesterday that the witness in question happens also to be married to a vice-president of Saatchi & Saatchi North America.
In London, a spokesman for the agency was reported as saying it had additional material to submit to the court. "We have considerably more evidence than just a lift man."