Lawyers acting for film director Roman Polanski say they will challenge his arrest in Switzerland and attempts to extradite him to the US.
Prosecutors in Los Angeles want the Paris-born Polish filmmaker returned, so that he can be sentenced for having sex with a 13-year-old girl in 1977.
He pleaded guilty at the time as part of a plea bargain but then fled abroad.
Polanski was detained on Saturday as he arrived in Zurich to receive a lifetime achievement award.
French Culture Minister Frederic Mitterrand said he had been "stunned" to hear about the arrest, and added that President Nicolas Sarkozy was following the case.
Mr Polanski, 76, has French citizenship.
In its Monday edition the French daily Le Figaro quotes his Paris-based lawyer as saying: "We will be demanding that he be freed. Then we will fight the extradition."
'No choice'
The director is being held under a 2005 international alert issued by the US.
CASE TIMELINE
1977 - Polanski admits unlawful sex with Samantha Geimer, 13, in Los Angeles
1978 - flees to Britain after US arrest warrant is issued
1978 - immediately moves to France where he holds citizenship
1978 - settles in France, where he is protected by France's limited extradition with US
2008 - Polanski's lawyer demands case be dismissed and hearing moved out of LA court
2009 - Polanski's request to have hearing outside LA is denied
Profile: Roman Polanski
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Swiss Justice Minister Eveline Widmer-Schlumpf said that because of agreements with the US, "when Mr Polanski arrived we had no choice from a legal point of view but to arrest him".
"He obviously has the right to appeal and I think he will do so," she added.
The filmmaker was initially indicted on six counts and faced up to life in prison. Has not set foot in the US for more than 30 years.
In recent years, he has tried to have the rape case dismissed, claiming the original judge, who is now dead, arranged a plea bargain but later reneged.
Mr Polanski has been to Switzerland before, but this time US authorities apparently knew of his trip in advance.
That gave them time to prepare the groundwork for his arrest and send a provisional arrest warrant to Swiss authorities, the Los Angeles district attorney's office said on Sunday.
The victim at the centre of the case, Samantha Geimer, has previously asked for the charges to be dropped.